JEE Physics

StemEZ

Chapter 2

Kinematics - all with Video Answers

Educators

Chapter Questions

Problem 166

A branch of physics dealing whit motion without considering its causes is known as ...
(A) Kinematics
(B) dynamics
(C) Hydrodynamics (D) mechanics

Muhammad Nawaz

Muhammad Nawaz

Numerade Educator

Problem 167

Mechanics is a branch of physics. This branch is ...
(A) Kinematics without dynamics
(B) dynamics without Kinematics
(C) Kinematics and dynamics
(D) Kinematics or dynamics

Muhammad Nawaz

Numerade Educator

Problem 168

To locate the position of the particle we need ...
(A) a frame of reference
(B) direction of the particle
(C) size of the particle
(D) mass of the particle

Muhammad Nawaz

Numerade Educator

Problem 169

Frame of reference is a $\ldots$ and a ... from where an observer takes his observation,
(A) place, size
(B) size, situation
(C) situation, size
(D) place, situation

Muhammad Nawaz

Numerade Educator

Problem 170

As shown in the figure a particle moves from 0 to $\mathrm{A}$, and then $\mathrm{A}$ to $\mathrm{B}$. Find path length and displacement.
(A) $2 \mathrm{~m},-2 \mathrm{~m}$
(B) $8 \mathrm{~m},-2 \mathrm{~m}$
(C) $2 \mathrm{~m}, 2 \mathrm{~m}$
(D) $8 \mathrm{~m},-8 \mathrm{~m}$

Prem Bijarniya

Numerade Educator

Problem 171

A particle moves from $A$ to $B$ and then it moves from $B$ to $C$ as shown in figure. Calculate the ratio between path length and displacement.

Prem Bijarniya

Numerade Educator

Problem 172

A particle moves from $\mathrm{A}$ to $\mathrm{P}$ and then it moves from $\mathrm{P}$ to $\mathrm{B}$
as shown in the figure. Find path length and displacement.
(A) $(21 / \sqrt{3}), 1$
(B) $(1 / \sqrt{3}), 1$
(C) 21,1
(D) $1,(21 / \sqrt{3})$

Prem Bijarniya

Numerade Educator

Problem 173

A car goes from one end to the other end of a semicircular path of diameter ' $\mathrm{d}$ '. Find the ratio between path length and displacement.
$\begin{array}{lll}\text { (A) }(3 \pi / 2) & \text { (B) } \pi \text { (C) } 2 & \text { (D) } \pi / 2\end{array}$

Muhammad Nawaz

Numerade Educator

Problem 174

A particle goes from point $\mathrm{A}$ to $\mathrm{B}$. Its displacement is $\mathrm{X}$ and path length is $\mathrm{y}$. So $\mathrm{x} / \mathrm{y} \ldots$
$(\mathrm{A})>1$
(B) $<1$
(C) $\geq 1$
(D) $\leq 1$

Muhammad Nawaz

Numerade Educator

Problem 175

As shown in the figure a particle starts its motion from 0 to $\mathrm{A}$. And then it moves from $\mathrm{A}$ to $\mathrm{B} \cdot \underline{\mathrm{AB}}$ is an arc find the Path length
(A) $2 \mathrm{r}$
(B) $\mathrm{r}+(\pi / 3)$
(C) $\mathrm{r}\{1+(\pi / 3)\}$
$(\mathrm{D})(\pi / 3)(\mathrm{r}+1)$

Prem Bijarniya

Numerade Educator

Problem 176

Here is a cube made from twelve wire each of length $1 .$ An ant goes from $\mathrm{A}$ to $\mathrm{G}$ through path $\mathrm{A}-\mathrm{B}-\mathrm{C}-\mathrm{G}$. Calculate the displacement (A) 31
(B) 21
(C) $\sqrt{31}$
(D) $(1 / \sqrt{3})$

Vysakh M

Numerade Educator

Problem 177

As shown in the figure particle P moves from $\mathrm{A}$ to $\mathrm{B}$ and particle $Q$ moves from $C$ to D. Displacements for $P$ and $Q$ are $\mathrm{x}$ and $\mathrm{y}$ respectively then
(A) $x>y$
(B) $x<y$
(C) $x=y$
(D) $\mathrm{x} \geq \mathrm{y}$

Prem Bijarniya

Numerade Educator

Problem 178

Shape of the graph of position $\rightarrow$ time given in the figure for a body shows that (A) The body moves with constant acceleration
(B) The body moves with zero velocity
(C) The body returns back towards the origin
(D) nothing can be said

Vysakh M

Numerade Educator

Problem 179

The graph of position $\rightarrow$ time shown in the figure for a particle is not possible because ...
(A) velocity cannot have two values at one time
(B) Displacement cannot have two values at one time
(C) Acceleration cannot have two values at one time
(D) A, B and C are true

Vysakh M

Numerade Educator

Problem 180

An ant goes from $\mathrm{P}$ to $\mathrm{Q}$ on a circular path in 20 second Radius $\mathrm{OP}=10 \mathrm{~m} .$ What is the average speed and average velocity of it?
(A) $(\pi / 6) \mathrm{ms}^{-1}, 3 \mathrm{~ms}^{-1}$
(B) $(\pi / 3) \mathrm{ms}^{-1},(\sqrt{3} / 2) \mathrm{ms}^{-1}$
(C) $(\pi / 3) \mathrm{ms}^{-1}, \sqrt{3} \mathrm{~ms}^{-1}$
(D) $\pi \mathrm{ms}^{-1}, \sqrt{6} \mathrm{~ms}^{-1}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 181

A particle is thrown in upward direction with initial velocity of $60 \mathrm{~m} / \mathrm{s}$. Find average speed and average velocity after 10 seconds. $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$
(A) $26 \mathrm{~ms}^{-1}, 16 \mathrm{~ms}^{-1}$
(B) $26 \mathrm{~ms}^{-1}, 10 \mathrm{~ms}^{-1}$
(C) $20 \mathrm{~ms}^{-1}, 10 \mathrm{~ms}^{-1}$
(D) $15 \mathrm{~ms}^{-1}, 25 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 182

The ratio of pathlength and the respective time interval is
(A) Mean Velocity
(B) Mean speed
(C) instantaneous velocity
(D) instantaneous speed

Muhammad Nawaz

Numerade Educator

Problem 183

A car moving over a straight path covers a distance $\mathrm{x}$ with constant speed $10 \mathrm{~ms}^{-1}$ and then the same distance with constant speed of $\mathrm{V}_{2}$. If average speed of the car is $16 \mathrm{~ms}^{-1}$, then $\mathrm{V}_{2}=\ldots$
(A) $30 \mathrm{~ms}^{-1}$
(B) $20 \mathrm{~ms}^{-1}$
(C) $40 \mathrm{~ms}^{-1}$
(D) $25 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 184

A bus travels between two points $\mathrm{A}$ and B. $\mathrm{V}_{1}$ and $\mathrm{V}_{2}$ are it average speed and average velocity then
(A) $\mathrm{v}_{1}>\mathrm{v}_{2}$
(B) $\mathrm{v}_{1}<\mathrm{v}_{2}$
(C) $\mathrm{v}_{1}=\mathrm{v}_{2}$
(D) depends on situation

Muhammad Nawaz

Numerade Educator

Problem 185

A car covers one third part of its straight path with speed $\mathrm{V}_{1}$ and the rest with speed $\mathrm{V}_{2}$. What is its average speed?
(A) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(2 \mathrm{v}_{1}+\mathrm{v}_{2}\right)\right]$
(B) $\left[\left(2 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(3 \mathrm{v}_{1}+\mathrm{v}_{2}\right)\right]$
(C) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(\mathrm{v}_{1}+2 \mathrm{v}_{2}\right)\right]$
(D) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(2 \mathrm{v}_{1}+2 \mathrm{v}_{2}\right)\right]$

Muhammad Nawaz

Numerade Educator

Problem 186

Rohit completes a semicircular path of radius $\mathrm{R}$ in 10 seconds. Calculate average speed and average velocity in $\mathrm{ms}^{-1}$
(A) $[(2 \pi R) / 10],(2 R / 10)$
(B) $(\pi R / 10),(\mathrm{R} / 10)$
(C) $(\pi R / 10),(2 R / 10)$
(D) $[(2 \pi R) / 10],(\mathrm{R} / 10)$

Muhammad Nawaz

Numerade Educator

Problem 187

A particle moves $4 \mathrm{~m}$ in the south direction. Then it moves $3 \mathrm{~m}$ in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity?
(A) $(5 / 7)$
(B) $(7 / 5)$
(C) $(14 / 5)$
(D) $(5 / 14)$

Muhammad Nawaz

Numerade Educator

Problem 188

A particle is projected vertically upwards with velocity $30 \mathrm{~ms}^{-1}$. Find the ratio of average speed and instantaneous velocity after 6 s. $\left[\mathrm{g}=10 \mathrm{~ms}^{-1}\right]$
(A) $(1 / 2)$
(B) 2
(C) 3
(D) 4

Muhammad Nawaz

Numerade Educator

Problem 189

The motion of a particle along a straight line is described by the function $\mathrm{x}=(3 \mathrm{t}-2)^{2}$. Calculate the acceleration after $10 \mathrm{~s}$.
(A) $9 \mathrm{~ms}^{-2}$
(B) $18 \mathrm{~ms}^{-2}$
(C) $36 \mathrm{~ms}^{-2}$
(D) $6 \mathrm{~ms}^{-2}$

Muhammad Nawaz

Numerade Educator

Problem 190

Given figure shows a graph at acceleration $\rightarrow$ time for a rectilinear motion. Find average acceleration in first 10 seconds.
(A) $10 \mathrm{~ms}^{-2}$
(B) $15 \mathrm{~ms}^{-2}$
(C) $75 \mathrm{~ms}^{-2}$
(D) $30 \mathrm{~ms}^{-2}$

Prem Bijarniya

Numerade Educator

Problem 191

A body starts its motion with zero velocity and its acceleration is $\left(3 \mathrm{~m} / \mathrm{s}^{2}\right)$. Find the distance travelled by it in fifth second.
(A) $15.5 \mathrm{~m}$
(B) $17.5 \mathrm{~m}$
(C) $13.5 \mathrm{~m}$
(D) $14.5 \mathrm{~m}$

Muhammad Nawaz

Numerade Educator

Problem 192

A body is moving in $\mathrm{x}$ direction with constant acceleration $\alpha$. Find the difference of the displacement covered by it in nth second and $(\mathrm{n}-1)$ th second.
(A) $\alpha$
(B) $(\alpha / 2)$
(C) $3 \alpha$
(D) $(3 / 2) \alpha$

Muhammad Nawaz

Numerade Educator

Problem 193

What does the speedometer measure kept in motorbike?
(A) Average Velocity
(B) Average speed
(C) instantaneous speed
(D) instantaneous Velocity

Muhammad Nawaz

Numerade Educator

Problem 194

The displacement of a particle in $\mathrm{x}$ direction is given by $\mathrm{x}=9-5 \mathrm{t}+4 \mathrm{t}^{2}$. Find the Velocity at time $\mathrm{t}=0$
(A) $-8 \mathrm{~ms}^{-1}$
(B) $-5 \mathrm{~ms}^{-1}$
(C) $3 \mathrm{~ms}^{-1}$
(D) $10 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 195

A freely falling particle covers a building of $45 \mathrm{~m}$ height in one second. Find the height of the point from where the particle was released. $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$
(A) $120 \mathrm{~m}$
(B) $125 \mathrm{~m}$
(C) $25 \mathrm{~m}$
(D) $80 \mathrm{~m}$

Muhammad Nawaz

Numerade Educator

Problem 196

The distance travelled by a particle is given by $\mathrm{s}=3+2 \mathrm{t}+5 \mathrm{t}^{2}$ The initial velocity of the particle is $\ldots$
(A) 2 unit
(B) 3 unit
(C) 10 unit
(D) 5 unit

Muhammad Nawaz

Numerade Educator

Problem 197

A particle is thrown in upward direction with Velocity $\mathrm{V}_{0}$. It passes through a point $\mathrm{p}$ of height $\mathrm{h}$ at time $\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ so $\mathrm{t}_{1}+\mathrm{t}_{2}=\ldots$
(A) $\left(\mathrm{v}_{0} / \mathrm{g}\right)$
(B) $\left[\left(2 \mathrm{v}_{0}\right) / \mathrm{g}\right]$
(C) $(2 \mathrm{~h} / \mathrm{g})$
(D) $(\mathrm{h} / 2 \mathrm{~g})$

Muhammad Nawaz

Numerade Educator

Problem 198

A particle is thrown in upward direction with initial velocity $\mathrm{V}_{0}$. It crosses point $\mathrm{P}$ at height $\mathrm{h}$ at time $\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ so $\mathrm{t}_{1} \mathrm{t}_{2}=-$
(A) $(2 \mathrm{~h} / \mathrm{g})$
(B) $\left[\left(\mathrm{V}_{0}^{2}\right) / 2 \mathrm{~g}\right]$
(C) $\left[\left(2 \mathrm{~V}_{0}^{2}\right) / \mathrm{g}\right]$
(D) $(\mathrm{h} / 2 \mathrm{~g})$

Muhammad Nawaz

Numerade Educator

Problem 199

Ball A is thrown in upward from the top of a tower of height
h. At the same time ball B starts to fall from that point. When A comes to the top of the tower, B reaches the ground. Find the time to reach maximum height for $\mathrm{A}$.
(A) $\sqrt{(\mathrm{h} / \mathrm{g})}$
(B) $\sqrt{(2 \mathrm{~h} / \mathrm{g})}$
(C) $\sqrt{(h / 2 g)}$
(D) $\sqrt{(4 \mathrm{~h} / \mathrm{g})}$

Muhammad Nawaz

Numerade Educator

Problem 200

In the figure Velocity $(\mathrm{V}) \rightarrow$ position graph is given. Find the true equation. $(\mathrm{A}) \mathrm{v}=\left(\mathrm{v}_{0} / \mathrm{x}_{0}\right) \mathrm{x}-\mathrm{v}_{0}$
(B) $v=-\left(v_{0} / x_{0}\right) x+v_{0}$
(C) $v=\left[\left(-v_{0}\right) / x_{0}\right] x-v_{0}$
(D) $v=\left(v_{0} / x_{0}\right) x+v_{0}$

Prem Bijarniya

Numerade Educator

Problem 201

In the figure there is a graph of $\mathrm{a} \rightarrow \mathrm{x}$ for a moving particle. Hence $(\mathrm{da} / \mathrm{dt})=\ldots \mathrm{V}$ (A) $\left(\mathrm{x}_{0} / \mathrm{a}_{0}\right)$
(B) $\left[\left(-\mathrm{x}_{0}\right) / \mathrm{a}_{0}\right]$
(C) $\left[\left(-a_{0}\right) / x_{0}\right]$
(D) $\left(\mathrm{a}_{0} / \mathrm{x}_{0}\right)$

Prem Bijarniya

Numerade Educator

Problem 202

A particle is moving in a straight line with initial velocity of $10 \mathrm{~ms}^{-1}$. A graph of acceleration $\rightarrow$ time of the particle is given in the figure. Find velocity at $\mathrm{t}=10 \mathrm{~s}$.
(A) $25 \mathrm{~ms}^{-1}$
(B) $35 \mathrm{~ms}^{-1}$
(C) $45 \mathrm{~ms}^{-1}$
(D) $15 \mathrm{~ms}^{-1}$

Vishal Gupta

Numerade Educator

Problem 203

A graph of moving body with constant acceleration is given in the figure. What is the velocity after time t? (A) $\mathrm{OA}+(\mathrm{DC} / \mathrm{BC}) \cdot \mathrm{OE}$
(B) $\mathrm{OA}+(\mathrm{DC} / \mathrm{BC}) \cdot \mathrm{DE}$
(C) $\mathrm{AB}+(\mathrm{BC} / \mathrm{DC}) \cdot \mathrm{OE}$
(D) $\mathrm{OA}+(\mathrm{DC} / \mathrm{BC}) \cdot \mathrm{AD}$

Vishal Gupta

Numerade Educator

Problem 204

The graph given in the figure shows that the body is moving with $\ldots \ldots$
(A) increasing acceleration
(B) decreasing acceleration
(C) constant velocity
(D) increasing velocity

Vysakh M

Numerade Educator

Problem 205

Slope of the velocity-time graph gives of a moving body.
(A) displacement
(B) acceleration
(C) initial velocity
(D) final velocity

Muhammad Nawaz

Numerade Educator

Problem 206

The intercept of the velocity-time graph on the velocity axis gives.
(A) initial velocity
(B) final velocity
(C) average velocity
(D) instantaneous velocity

Muhammad Nawaz

Numerade Educator

Problem 207

Here are the graphs of velocity $\rightarrow$ time of two cars $\mathrm{A}$ and $\mathrm{B}$, Find the ratio of the acceleration after time t.
(A) $(1 / \sqrt{3})$
(B) $(1 / 3)$
(C) $\sqrt{3}$
(D) 3

Vishal Gupta

Numerade Educator

Problem 208

Here is a velocity - time graph of a motorbike moving in one direction. Calculate the distance covered by it in last two seconds.
(A) $5 \mathrm{~m}$
(B) $20 \mathrm{~m}$
(C) $50 \mathrm{~m}$
(D) $25 \mathrm{~m}$

Vysakh M

Numerade Educator

Problem 209

In the above figure acceleration (a) $\rightarrow$ time (t) graph is given. Hence $\mathrm{V} \alpha \ldots \ldots$
(A) a
(B) $\sqrt{a}$
(C) $\mathrm{a}^{2}$
(D) $\mathrm{a}^{3}$

Vishal Gupta

Numerade Educator

Problem 210

The graph of displacent $(\mathrm{x}) \rightarrow$ time $(\mathrm{t})$ for an object is given in the figure. In which part of the graph the acceleration of the particle is positive ? (A) $\mathrm{OA}$
(B) $\mathrm{AB}$
(C) $0-\mathrm{A}-\mathrm{B}$
(D) acceleration is not positive at any part.

Vysakh M

Numerade Educator

Problem 211

In a uniformly accelerated motion the slope of velocity - time graph gives ....
(A) The instantaneous velocity
(B) The acceleration
(C) The initial velocity
(D) The final velocity

Muhammad Nawaz

Numerade Educator

Problem 212

The area covered by the curve of $\mathrm{V}-\mathrm{t}$ graph and time axis is equal to magnitude of $\ldots$
(A) change in velocity
(B) change in acceleration
(C) displacement
(D) final velocity

Muhammad Nawaz

Numerade Educator

Problem 213

An object moves in a straight line. It starts from the rest and its acceleration is $2 \mathrm{~ms}^{-2}$. After reaching a certain point it comes back to the original point. In this movement its acceleration is $-3 \mathrm{~ms}^{-2}$. till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.
(A) $6 \mathrm{~ms}^{-1}$
(B) $5 \mathrm{~ms}^{-1}$
(C) $10 \mathrm{~ms}^{-1}$
(D) $4 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 214

The relation between time and displacement of a moving particle is given by $t=2 \alpha x^{2}$ where $\alpha$ is a constant. The shape of the graph $\mathrm{x} \rightarrow \mathrm{y}$ is
(A) parabola
(B) hyperbola
(C) ellipse
(D) circle

Muhammad Nawaz

Numerade Educator

Problem 215

Here are the graphs of $\mathrm{x} \rightarrow \mathrm{t}$ of a moving body. Which of them is not suitable ?

Vysakh M

Numerade Educator

Problem 216

Here are the graphs of $\mathrm{v} \rightarrow \mathrm{t}$ of a moving body. Which of them is not suitable?

Vysakh M

Numerade Educator

Problem 217

Comprehension type questions
In the figure is a graph of velocity $\rightarrow$ time for a particle.
Which area shows the displacement covered by the particle after time t
(A) closed fig AODCA
(B) closed fig. ABCA
(C) closed fig. AODCBA
(D) none of above

Vishal Gupta

Numerade Educator

Problem 218

Comprehension type questions In the figure is a graph of velocity $\rightarrow$ time for a particle.
Which part shows initial velocity of the particle?
(A) $\mathrm{OA}$
(B) $\mathrm{AB}$
(C) $\mathrm{AC}$
(D) $\mathrm{AOA}$

Vysakh M

Numerade Educator

Problem 219

Comprehension type questions In the figure is a graph of velocity $\rightarrow$ time for a particle.
How will you calculate the acceleration of the particle?
(A) taking length of $\mathrm{AB}$
(B) taking magnitude of $\mathrm{BC}$
(C) taking slope of $\mathrm{AC}$
(D) taking slope of $\mathrm{AB}$

Vysakh M

Numerade Educator

Problem 220

Given graph shows relation between position and time. Find correct graph of acceleration $\rightarrow$ time

Vishal Gupta

Numerade Educator

Problem 221

Here are displacement $\rightarrow$ time graphs of particle $\mathrm{A}$ and $\mathrm{B}$. If $\mathrm{V}_{\mathrm{A}}$ and $\mathrm{V}_{\mathrm{B}}$ are velocities of the particles respectively, then $\left(\mathrm{V}_{\mathrm{A}} / \mathrm{V}_{\mathrm{B}}\right)=\ldots$
(A) $(1 / 3)$
(B) 3
(C) $(1 / \sqrt{3})$
(D) $\sqrt{3}$

Vishal Gupta

Numerade Educator

Problem 222

Given graph shows relation between position $(\mathrm{x}) \rightarrow$ time $(\mathrm{t})$ Find the correct graph of velocity $\rightarrow$ time.

Vishal Gupta

Numerade Educator

Problem 223

Particles $\mathrm{A}$ and $\mathrm{B}$ are released from the same height at an interval of $2 \mathrm{~s}$. After some time $t$ the distance between $\mathrm{A}$ and $\mathrm{B}$ is $100 \mathrm{~m}$. Calculate time t.
(A) $8 \mathrm{~s}$
(B) $6 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $12 \mathrm{~s}$

Muhammad Nawaz

Numerade Educator

Problem 224

As shown in the figure a particle is released from $P$. It reaches at point $\mathrm{Q}$ at time $\mathrm{t}_{1}$ and reaches at point $\mathrm{R}$ at time
$\mathrm{t}_{2}$ so $\left(\mathrm{t}_{1} / \mathrm{t}_{2}\right)=\ldots$
$(\mathrm{A})+(1 / 3)$
(B) $-(5 / 6)$
(C) $(2 / 1)$
(D) $(4 / 1)$

Vishal Gupta

Numerade Educator

Problem 225

A particle moves in straight line. Its position is given by $\mathrm{x}=2+5 \mathrm{t}-3 \mathrm{t}^{2}$. Find the ratio of initial velocity and initial acceleration.
$(\mathrm{A})+(5 / 6)$
(B) $-(5 / 6)$
(C) $(6 / 5)$
(D) $-(6 / 5)$

Muhammad Nawaz

Numerade Educator

Problem 226

A particle is moving in a circle of radius $\mathrm{R}$ with constant speed. It covers an angle $\theta$ in some time interval. Find displacement in this interval of time.
(A) $2 \mathrm{R} \cos (\theta / 2)$
(B) $2 \operatorname{Rsin}(\theta / 2)$
(C) $2 \mathrm{R} \cos \theta$
(D) $2 \mathrm{R} \sin \theta$

Muhammad Nawaz

Numerade Educator

Problem 227

A particle is moving in a straight line with initial velocity of $200 \mathrm{~ms}^{-1}$ acceleration of the particle is given by $\mathrm{a}=3 \mathrm{t}^{2}-2 \mathrm{t}$. Find velocity of the particle at 10 second.
(A) $1100 \mathrm{~ms}^{-1}$
(B) $300 \mathrm{~ms}^{-1}$
(C) $900 \mathrm{~ms}^{-1}$
(D) $100 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 228

Angle of projection, maximum height and time to reach the maximum height of a particle are $\theta, \mathrm{H}$ and $\mathrm{tm}$ respectively. Find the true relation.
(A) $\mathrm{t}_{\mathrm{m}}=\sqrt{(\mathrm{H} / 2 \mathrm{~g})}$
(B) $\mathrm{t}_{\mathrm{m}}=\sqrt{(2 \mathrm{H} / \mathrm{g})}$
(C) $\mathrm{t}_{\mathrm{m}}=\sqrt{(4 \mathrm{H} / \mathrm{g})}$
(D) $t_{\mathrm{m}}=\sqrt{(\mathrm{H} / 4 \mathrm{~g})}$

Muhammad Nawaz

Numerade Educator

Problem 229

Particle A is projected vertically upward from a top of a tower. At the same time particle $B$ is dropped from the same point. The graph of distance (s) between the two particle varies with time is.

Yuva S

Numerade Educator

Problem 230

A car is moving with speed $30 \mathrm{~m}$. Due to application of brakes it travels $30 \mathrm{~m}$ before stopping. Find its acceleration.
(A) $15 \mathrm{~m} / \mathrm{s}^{2}$
(B) $-15 \mathrm{~m} / \mathrm{s}^{2}$
(C) $30 \mathrm{~m} / \mathrm{s}^{2}$
(D) $10 \mathrm{~m} / \mathrm{s}^{2}$

Muhammad Nawaz

Numerade Educator

Problem 231

A particle moves with a constant acceleration $\left(2 \mathrm{~m} / \mathrm{s}^{2}\right)$ Its initial velocity is $10 \mathrm{~m} / \mathrm{s}$. Find velocity after $\mathrm{t}$ second.
(A) $(10+\mathrm{t}) \mathrm{ms}^{-1}$
(B) $5(2+\mathrm{t}) \mathrm{ms}^{-1}$
(C) $2(5+\mathrm{t}) \mathrm{ms}^{-1}$
(D) $\left(10+\mathrm{t}^{2}\right) \mathrm{ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 232

A balloon is going vertically up with velocity $12 \mathrm{~m} / \mathrm{s}$. When it is at height of $65 \mathrm{~m}$ above the ground, it releases a stone. In how much time the stone will reach the ground.
(A) $\sqrt{13} \mathrm{~s}$
(B) $10 \mathrm{~s}$
(C) $5 \mathrm{~s}$
(D) $6 \mathrm{~s}$

Muhammad Nawaz

Numerade Educator

Problem 233

A particle moves with constant acceleration $2 \mathrm{~m} / \mathrm{s}^{2}$ in $\mathrm{x}$ direction. The distance travelled in fifth second is $19 \mathrm{~m}$. Calculate the distance travelled after 5 second.
(A) $50 \mathrm{~m}$
(B) $75 \mathrm{~m}$
(C) $80 \mathrm{~m}$
(D) $70 \mathrm{~m}$

Muhammad Nawaz

Numerade Educator

Problem 234

Two bodies of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ are dropped from heights $\mathrm{H}$ and $2 \mathrm{H}$ respectively. The ratio of time taken by the bodies to touch the ground is ...
(A) $(1 / 2)$
(B) 2
(C) $(1 / \sqrt{2})$
(D) $(\sqrt{2} / 1)$

Muhammad Nawaz

Numerade Educator

Problem 235

A freely falling stone crashes through a horizontal glass plate at time $t$ and losses half of its velocity. After time $(t / 2)$ it falls on the ground. The glass plate is $60 \mathrm{~m}$ high from the ground. Find the total distance travelled by the stone. $\left[g=10 \mathrm{~ms}^{-2}\right]$
(A) $120 \mathrm{~m}$
(B) $80 \mathrm{~m}$
(C) $100 \mathrm{~m}$
(D) $140 \mathrm{~m}$

Penny Riley

Numerade Educator

Problem 236

A freely falling object travels distance $\mathrm{H}$. Its velocity is $\mathrm{V}$. Hence, in travelling further distance of $4 \mathrm{H}$ its velocity will become ...
(A) $\sqrt{3} \mathrm{~V}$
(B) $\sqrt{5} \mathrm{~V}$
(C) $2 \mathrm{~V}$
(D) $3 \mathrm{~V}$

Muhammad Nawaz

Numerade Educator

Problem 237

A ball is thrown vertically upward direction. Neglecting the air resistance velocity of the ball in air will
(A) zero
(B) decrease when it is going up
(C) decrease when it is coming down
(D) remain constant

Muhammad Nawaz

Numerade Educator

Problem 238

Two particles $\mathrm{P}$ and $\mathrm{Q}$ get $5 \mathrm{~m}$ closer each second while travelling in opposite direction. They get $1 \mathrm{~m}$ closer each second while travelling in same direction. The speeds of $\mathrm{P}$ and $\mathrm{Q}$ are respectively
(A) $5 \mathrm{~ms}^{-1}, 1 \mathrm{~ms}^{-1}$
(B) $3 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}$
(C) $3 \mathrm{~ms}^{-1}, 2 \mathrm{~ms}^{-1}$
(D) $10 \mathrm{~ms}^{-1}, 5 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 239

Motion of a particle is described by an equation $\mathrm{v}=(\mathrm{A}+\mathrm{y})^{(1 / 2)}$ where $\mathrm{v}, \mathrm{y}$ and $\mathrm{A}$ are velocity distance and a constant respectively. Find the acceleration of the particle.
(A) 1 unit
(B) 2 unit
(C) $(1 / 2)$ unit
(D) 3 unit

Muhammad Nawaz

Numerade Educator

Problem 240

The minimum distance in which a car can be stopped is $\mathrm{x}$. The velocity of the car is $\mathrm{V}$. If the velocity is $2 \mathrm{~V}$ then find the stopping distance.
(A) $2 \mathrm{x}$
(B) $4 \mathrm{x}$
(C) $3 \mathrm{x}$
(D) $(1 / 2) \mathrm{x}$

Muhammad Nawaz

Numerade Educator

Problem 241

A particle moves in one direction with acceleration $2 \mathrm{~ms}^{-2}$ and initial velocity $3 \mathrm{~ms}^{-1}$.After what time its displacement will be $10 \mathrm{~m}$ ?
(A) $1 \mathrm{~s}$
(B) $2 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $4 \mathrm{~s}$

Muhammad Nawaz

Numerade Educator

Problem 242

A goods train is moving with constant acceleration. When engine passes through a signal its speed is U. Midpoint of the train passes the signal with speed $\mathrm{V}$. What will be the speed of the last wagon?
(B) $\left.\sqrt{[}\left(\mathrm{V}^{2}-\mathrm{U}^{2}\right) / 2\right]$
(D) $\sqrt{[}\left(2 \mathrm{~V}^{2}-\mathrm{U}^{2}\right)$

Muhammad Nawaz

Numerade Educator

Problem 243

Displacement of a particle in y direction is given by $\mathrm{y}=\mathrm{t}^{2}-5 \mathrm{t}+5$ where $\mathrm{t}$ is in second. Calculate the time when its velocity is zero.
(A) $5 \mathrm{~s}$
(B) $2.5 \mathrm{~s}$
(C) $10 \mathrm{~s}$
(D) $3 \mathrm{~s}$

Muhammad Nawaz

Numerade Educator

Problem 244

The area under acceleration versus time graph for any time interval represents...
(A) Initial velocity
(B) final velocity
(C) change in velocity in the time interval
(D) Distance covered by the particle

Muhammad Nawaz

Numerade Educator

Problem 245

A ball is thrown vertically upward. What is the velocity and acceleration of the ball at the maximum height?
(A) $-$ gt $\mathrm{ms}^{-1}, 0$
(B) $0,-9 \mathrm{~ms}^{-2}$
(C) $\mathrm{g} \mathrm{ms}^{-1}, 0$
(D) $0,-\mathrm{gt} \mathrm{ms}^{-2}$

Muhammad Nawaz

Numerade Educator

Problem 246

The relation between velocity and position of a particle is $\mathrm{V}=\mathrm{Ax}+\mathrm{B}$ where $\mathrm{A}$ and $\mathrm{B}$ are constants. Acceleration of the particle is $10 \mathrm{~ms}^{-2}$ when its velocity is $\mathrm{V}$, How much is the acceleration when its velocity is $2 \mathrm{~V}$
(A) $20 \mathrm{~ms}^{-2}$
(B) $10 \mathrm{~ms}^{-1}$
(C) $5 \mathrm{~ms}^{-2}$
(D) 0

Muhammad Nawaz

Numerade Educator

Problem 247

A particle moves on a plane along the path $\mathrm{y}=\mathrm{Ax}^{3}+\mathrm{B}$ in such a way that $(\mathrm{dx} / \mathrm{dt})=\mathrm{c} . \mathrm{c}, \mathrm{A}, \mathrm{B}$ are constant. Calculate the acceleration of the particle.
(A) $3 \mathrm{Ax} \mathrm{cj} \mathrm{ms}^{-2}$
(B) $6 \mathrm{Axc}^{2} \hat{\mathrm{j}} \mathrm{ms}^{-2}$
(C) $3 \mathrm{Axc}^{2} \hat{\mathrm{j}} \mathrm{ms}^{-2}$
(D) $\left[c \hat{i}+3 A x c^{2} \hat{j}\right] m s^{-2}$

Muhammad Nawaz

Numerade Educator

Problem 248

A particle is at $\mathrm{x}=0$ at time $\mathrm{t}=0 .$ It starts moving along positive $x$ direction with velocity $V=\alpha \sqrt{x}$ where $\alpha$ is constant. The displacement of particle varies with time as
(A) $\mathrm{t}^{4}$
(B)
(C) $\mathrm{t}^{2}$
(D) $t^{3}$

Muhammad Nawaz

Numerade Educator

Problem 249

An object moves in $\mathrm{x}-\mathrm{y}$ plane. Equations for displacement in $\mathrm{x}$ and $\mathrm{y}$ direction are $\mathrm{x}=3 \sin 2 \mathrm{t}$ and $\mathrm{y}=3 \cos 2 \mathrm{t}$ Speed of
the particle is
(A) zero
(B) constant and nonzero
(C) increasing with time t (D) decreasing with time t

Muhammad Nawaz

Numerade Educator

Problem 250

Motion of a particle is described by $\mathrm{x}=(\mathrm{t}-2)^{2}$ Find its velocity when it passes through origin.
(A) $0 \mathrm{~m} / \mathrm{s}$
(B) $2 \mathrm{~ms}^{-1}$
(C) $4 \mathrm{~ms}^{-1}$
(D) $8 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 251

To introduce a vector quantity ....
(A) it needs magnitude not direction
(B) it needs direction not magnitude
(C) it needs both magnitude and direction
(D) nothing is needed

Muhammad Nawaz

Numerade Educator

Problem 252

Which pair of two vectors is anti parallel

Muhammad Nawaz

Numerade Educator

Problem 253

In the above figure $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are two vectors. What from followings is true
(A) $\mathrm{P}^{\rightarrow}$ and $\mathrm{Q}^{\rightarrow}$ are equal
(B) $\mathrm{P}^{\rightarrow}$ and $\mathrm{Q}^{\rightarrow}$ are perpendicular
(C) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are anti parallel
(D) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are in same direction

Vysakh M

Numerade Educator

Problem 254

Which from the following is a scalar?
(A) Electric current
(B) Velocity
(C) acceleration
(D) Electric field

Muhammad Nawaz

Numerade Educator

Problem 255

$\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are equal vectors what from the followings is true.
(A) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are anti parallel
(B) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are parallel
(C) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ may be perpendicular
(D) $\mathrm{P}^{-}$ and $\mathrm{Q}^{\rightarrow}$ may be free vectors

Muhammad Nawaz

Numerade Educator

Problem 256

$\mathrm{P}^{\rightarrow}=\mathrm{Q}^{\rightarrow}$ is true, if $\ldots$
(A) their magnitudes are equal
(B) they are in same direction
(C) their magnitudes are equal and they are in same direction
(D) their magnitudes are not equal and they are not in same direction

Muhammad Nawaz

Numerade Educator

Problem 257

$\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ are in opposite direction so they are
(A) parallel vectors
(B) anti parallel vector
(C) equal vector
(D) perpendicular vector

Muhammad Nawaz

Numerade Educator

Problem 258

$\mathrm{A}^{\boldsymbol{\longrightarrow}}=1^{\wedge}+2 \hat{\mathrm{j}}+2 \mathrm{k}^{\wedge}$. Calculate the angle between $\mathrm{A}^{\rightarrow}$ and $\mathrm{Y}$
axis.
(A) $\sin ^{-1}(\sqrt{5} / 3)$
(B) $\sin ^{-1}(1 / \sqrt{3})$
(C) $\sin -1(\sqrt{10} / 3)$ (D) $\cos ^{-1}(\sqrt{5} / 3)$

Muhammad Nawaz

Numerade Educator

Problem 259

$\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ are nonzero vectors. Which from the followings is true ?
(A) $\left|\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}\right|^{2}-\left|\mathrm{A}^{\rightarrow}-\mathrm{B}^{\rightarrow}\right|^{2}=2\left(\mathrm{~A}^{2}+\mathrm{B}^{2}\right)$
(B) $\left|\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}\right|^{2}-\left|\mathrm{A}^{\rightarrow}-\mathrm{B}^{\rightarrow}\right|^{2}=2\left(\mathrm{~A}^{2}+\mathrm{B}^{2}\right)$
(C) $\left|\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}\right|^{2}-\left|\mathrm{A}^{\rightarrow}-\mathrm{B}^{\rightarrow}\right|^{2}=\mathrm{A}^{2}+\mathrm{B}^{2}$
(D) $\left|\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}\right|^{2}-\left|\mathrm{A}^{\rightarrow}-\mathrm{B}^{\rightarrow}\right|^{2}=\mathrm{A}^{2}-\mathrm{B}^{2}$

Muhammad Nawaz

Numerade Educator

Problem 260

$\mathrm{C}^{\rightarrow}=\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}$ and $\mathrm{A}=\mathrm{B}=\mathrm{C}$ Find the angle between
$\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{-}$
$(\mathrm{A})(\pi / 3)$
(B) $(\pi / 6)$
(C) $(2 \pi / 3)$
(D) 0

Muhammad Nawaz

Numerade Educator

Problem 261

The resultant of two vectors is maximum when they.
(A) are at right angles to each other
(B) act in opposite direction
(C) act in same direction
(D) are act $120^{\circ}$ to each other

Muhammad Nawaz

Numerade Educator

Problem 262

The resultant of two vectors $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$
(A) can be smaller than $\mathrm{A}-\mathrm{B}$ in magnitude
(B) can be greater than $\mathrm{A}+\mathrm{B}$ in magnitude
(C) can't be greater than $\mathrm{A}+\mathrm{B}$ or smaller than $\mathrm{A}-\mathrm{B}$ in magnitude
(D) none of above is true

Muhammad Nawaz

Numerade Educator

Problem 263

The resultant of two forces of magnitude $2 \mathrm{~N}$ and $3 \mathrm{~N}$ can never be.
(A) $4 \mathrm{~N}$
(B) $1 \mathrm{~N}$
(C) $2.5 \mathrm{~N}$
(D) $(1 / 2) \mathrm{N}$

Muhammad Nawaz

Numerade Educator

Problem 264

The sum of $\mathrm{P}^{\rightarrow}$ and $\mathrm{Q}^{\rightarrow}$ is at right angles to their difference then
(A) $\mathrm{A}=\mathrm{B}$
(B) $\mathrm{A}=2 \mathrm{~B}$
(C) $\mathrm{B}=2 \mathrm{~A}$
D) $A=B=A-B$

Muhammad Nawaz

Numerade Educator

Problem 265

Magnitudes of $\mathrm{A}^{\rightarrow}, \mathrm{B}^{\rightarrow}$ and $\mathrm{C}^{\rightarrow}$ are 41,40 and 9 respectively, $\mathrm{A}^{\rightarrow}=\mathrm{B}^{\rightarrow}+\mathrm{C}^{\rightarrow}$ Find the angle between $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$
(A) $\sin ^{-1}(9 / 40)$
(B) $\cos ^{-1}(9 / 41)$
(C) $\tan ^{-1}(9 / 41)$
(D) $\tan ^{-1}(41 / 40)$

Mahendra K

Numerade Educator

Problem 266

If $\mathrm{A}^{\rightarrow}=3 \hat{1}+4 \hat{\jmath}+9 \mathrm{k}$ is multiplied by 3 , then the component of the new vector along $\mathrm{z}$ direction is ..
(A) $-3$
(B) $+3$ $\begin{array}{ll}\text { (C) }-27 & \text { (D) }+27\end{array}$

Muhammad Nawaz

Numerade Educator

Problem 267

$\mathrm{A}^{-}+\mathrm{B}^{-}$ is perpendicular to $\mathrm{A}^{-}$ and $\left|\mathrm{B}^{-}\right|=2\left|\mathrm{~A}^{-}+\mathrm{B}^{-}\right|$ What
is the angle between $\mathrm{A}^{-}$ and $\mathrm{B}^{\rightarrow}$
$(\mathrm{A})(\pi / 6)$
(B) $(5 \pi / 6)$
(C) $(2 \pi / 3)$
(D) $(\pi / 3)$

Muhammad Nawaz

Numerade Educator

Problem 268

Out of the following pairs of forces, the resultant of which can not be $18 \mathrm{~N}$
(A) $11 \mathrm{~N}, 7 \mathrm{~N}$
(B) $11 \mathrm{~N}, 8 \mathrm{~N}$
(C) $11 \mathrm{~N}, 29 \mathrm{~N}$
(D) $11 \mathrm{~N}, 5 \mathrm{~N}$

Muhammad Nawaz

Numerade Educator

Problem 269

$ \mathrm{A}^{\rightarrow}=3 \hat{\imath}+2 \hat{\jmath}-5 \mathrm{k}^{\wedge}$ and $\mathrm{B}^{\rightarrow}=\hat{\imath}+\hat{\jmath}+2 \mathrm{k}^{\wedge}$ Find $\left|\mathrm{A}^{\rightarrow}+2 \mathrm{~B}^{\rightarrow}\right|$
(A) $\sqrt{40}$
(B) $\sqrt{42}$
(C) $\sqrt{39}$
(D) 2

Muhammad Nawaz

Numerade Educator

Problem 270

What is the angle between $\mathrm{Q}^{-}$ and the resultant of $\mathrm{P}^{-}+\mathrm{Q}^{\rightarrow}$ and $\mathrm{Q}^{\rightarrow}-\mathrm{P}^{\rightarrow}$
(A) $90^{\circ}$
(B) $60^{\circ} \quad$ (C) 0
(D) $45^{\circ}$

Muhammad Nawaz

Numerade Educator

Problem 271

$\mathrm{A}^{\boldsymbol{\longrightarrow}}=2 \mathrm{i} \wedge+2 \mathrm{j} \wedge-\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=2 \mathrm{i} \wedge-\mathrm{j} \wedge-2 \mathrm{k} \wedge$ Find $3 \mathrm{~A}^{\rightarrow}-2 \mathrm{~B}^{\rightarrow}$
(A) $2 \mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$
(B) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge-\mathrm{k} \wedge$
(C) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge+\mathrm{k} \wedge$
(D) $\mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$

Muhammad Nawaz

Numerade Educator

Problem 272

Linear momentum of a particle is $(3 \mathrm{i} \wedge+2 \mathrm{j} \wedge-\mathrm{k} \wedge) \mathrm{kg} \mathrm{ms}^{-1}$. Find
its magnitude.
(A) $\sqrt{14}$
(B) $\sqrt{12}$
(C) $\sqrt{15}$
(D) $\sqrt{11}$

Muhammad Nawaz

Numerade Educator

Problem 273

$\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}=\mathrm{C}^{-}$, Then $\mathrm{C}^{\rightarrow}$ is perpendicular to
(A) $\mathrm{A}^{\rightarrow}$ only
(B) $\mathrm{B}^{\rightarrow}$ only
(C) $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ both when the angle between them is $\ldots$
(D) $\mathrm{A}^{-}$ and $\mathrm{B}^{\rightarrow}$ both whatever to be the angle between them

Muhammad Nawaz

Numerade Educator

Problem 274

If $\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}=0$ then
(A) $\left|\mathrm{A}^{\rightarrow}\right|$ must be zero
(B) $\mathrm{B}^{\rightarrow} \mid$ must be zero
(C) either $\mathrm{A}^{\rightarrow}=0, \mathrm{~B}^{\rightarrow}=0$ or $\theta=0$
(D) either $\mathrm{A}^{\rightarrow}=0, \mathrm{~B}^{\rightarrow}=0$ or $\theta=(\pi / 2)$

Muhammad Nawaz

Numerade Educator

Problem 275

$\mathrm{y}$ component of $\mathrm{A} \rightarrow \times \mathrm{B}^{-}$ is.
$\mathrm{A}^{\rightarrow}=\mathrm{Ax} \hat{\imath}+\mathrm{Ay} \hat{\mathrm{j}}+\mathrm{A} z \mathrm{k}^{\wedge}$
$\mathrm{B}^{\rightarrow}=\mathrm{Bx} \hat{1}+\mathrm{By} \hat{\jmath}+\mathrm{Bzk}^{\wedge}$
(A) $A x B y-A y B x$
(B) $\mathrm{Az} \mathrm{Bx}-\mathrm{AxBz}$
(C) $\mathrm{AxBz}-\mathrm{AzBx}$
(D) $\mathrm{AzBy}-\mathrm{AyBz}$

Muhammad Nawaz

Numerade Educator

Problem 276

If A $\rightarrow \times B^{-}=0$ then $\mathrm{A}^{-} \cdot \mathrm{B}^{\rightarrow}=$
(A) $\mathrm{AB}$
(B) $(\mathrm{A} / \mathrm{B})$
(C) $(1 / 2) \mathrm{AB}$
(D) 0

Muhammad Nawaz

Numerade Educator

Problem 277

If $\mathrm{A}^{\rightarrow}=4 \mathrm{i} \wedge+3 \mathrm{j} \wedge-2 \mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=8 \mathrm{i} \wedge+6 \mathrm{j} \wedge-4 \mathrm{k} \wedge$ the angle
between $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ is
(A) $45^{\circ}$
(B) $0^{\circ}$
(C) $60^{\circ}$
(D) $90^{\circ}$

Muhammad Nawaz

Numerade Educator

Problem 278

$ \quad \mathrm{A}^{\rightarrow}=2 \mathrm{i} \wedge-3 \mathrm{j} \wedge+\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=8 \mathrm{i} \wedge-6 \mathrm{j} \wedge-4 \mathrm{k} \wedge$ then $\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|=\ldots$
(A) 28
(B) 14
(C) $39.8$
(D) 7

Muhammad Nawaz

Numerade Educator

Problem 279

If $\mathrm{A}^{\rightarrow}=2 \mathrm{i} \wedge+5 \mathrm{j} \wedge-\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=3 \mathrm{i} \wedge-2 \mathrm{j} \wedge-4 \mathrm{k} \wedge$ the angle
between $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ is
(A) 0
(B) $(\pi / 2)$
(C) $(\pi / 4)$
(D) $(\pi / 6)$

Muhammad Nawaz

Numerade Educator

Problem 280

Which statement is true ?
(A) $\mathrm{A} \rightarrow \times \mathrm{B}^{\rightarrow}=\mathrm{B}^{\rightarrow} \times \mathrm{A}^{\rightarrow}$
(B) $\mathrm{A} \rightarrow \times \mathrm{B}^{\rightarrow}=-\mathrm{B}^{-} \times \mathrm{A}^{\rightarrow}$
(C) $\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}=-\mathrm{B}^{\rightarrow} \cdot \mathrm{A}^{\rightarrow}$
(D) $\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}=\mathrm{AB}$

Muhammad Nawaz

Numerade Educator

Problem 281

Which from the following is true?
(A) $\cos \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) / \mathrm{AB}\right]$
(B) $\sin \theta=\left[\left(\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}\right) / \mathrm{AB}\right]$
(C) $\tan \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) /\left(\mathrm{A}^{-}-\mathrm{B}^{-}\right)\right]$
(D) $\cot \theta=\left[\mathrm{AB} /\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right)\right]$

Srilakshmi E K

Numerade Educator

Problem 282

$\quad\left(\mathrm{A}^{\rightarrow}+\mathrm{B}^{\rightarrow}\right) \cdot\left(\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right)=\ldots$
(A) 0
(B) $A^{2}+B^{2}$
(C) $\sqrt{\left(A^{2}+B^{2}\right)}$
(D) $\mathrm{A}^{2} \mathrm{~B}^{2}$

Dheeraj Sharma

Numerade Educator

Problem 283

The angle between $i \wedge+j \wedge$ and $z$ axis is $\ldots$
(A) 0
(B) 45
(C) 90
(D) 180

Muhammad Nawaz

Numerade Educator

Problem 284

$\mathrm{A} \overrightarrow{\mathrm{r}}=2 \mathrm{i} \wedge-\mathrm{j} \wedge+2 \mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=-\mathrm{i} \wedge-2 \mathrm{j} \wedge+4 \mathrm{k} \wedge$ what is the angle
between $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$
(A) $\cos ^{-1} 0.8888$
(B) $\cos ^{-1} 0.4444$
(C) $\sin ^{-1} 0.4444$
(D) $\sin ^{-1} 0.8888$

Muhammad Nawaz

Numerade Educator

Problem 285

$\mathrm{A}^{\boldsymbol{\rightarrow}}=\mathrm{Pi} \wedge-2 \mathrm{P}_{j} \wedge-\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=-3 \mathrm{i} \wedge+2 \mathrm{j} \wedge-14 \mathrm{k} \wedge$ are
perpendicular to each other. Then $p=\ldots$
(A) 3
(B) 4 $\begin{array}{ll}\text { (C) } 2 & \text { (D) } 1\end{array}$

Muhammad Nawaz

Numerade Educator

Problem 286

In the above triangle $\mathrm{AC}=5, \mathrm{BC}=8$ and $\mathrm{B}=(\pi / 6)$ Find the value of angle $\mathrm{A}$.
(A) $\sin ^{-1} 0.6$
(B) $\sin ^{-1} 0.8$
(C) $\sin ^{-1} 0.12$
(D) $\sin ^{-1} 0.4$

Vishal Gupta

Numerade Educator

Problem 287

$\mathrm{A}=+\mathrm{i} \wedge+\mathrm{j} \wedge-2 \mathrm{k} \wedge$ and $\mathrm{B} \overrightarrow{\mathrm{i}} \wedge-\mathrm{j} \wedge+\mathrm{k} \wedge$ Find the unit vector in
direction of $\mathrm{A} \rightarrow \times \mathrm{B}^{\rightarrow}$
(A) $[1 / \sqrt{(23)}](-\mathrm{i} \wedge-5 \mathrm{j} \wedge-2 \mathrm{k} \wedge)$
(B) $[1 / \sqrt{(35)]}(-\mathrm{i} \wedge-5 \mathrm{j} \wedge-3 \mathrm{k} \wedge)$
(C) $[1 / \sqrt{(29})](-i \wedge-5 j \wedge-3 k \wedge)$
(D) $[1 / \sqrt{(35)]}(-\mathrm{i} \wedge-5 j \wedge-3 \mathrm{k} \wedge)$

Muhammad Nawaz

Numerade Educator

Problem 288

What is unit vector along $\hat{i}+\hat{\jmath}$ ?
(A) $[(1+\hat{j}) / 2]$
(C) $[(\hat{1}+\hat{j}) / \sqrt{3}]$
(D) $[(\hat{1}-\hat{j}) / \sqrt{2}]$

Muhammad Nawaz

Numerade Educator

Problem 289

Unit vector of $\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}$ is $\mathrm{k}^{\wedge}$. Unit vector of $\mathrm{A}^{\rightarrow}$ is $\hat{1}$ Then what is the unit vector of $\mathrm{B}^{\rightarrow}$
(A) $\hat{\jmath}$
(B) - \hat?
(C) any unit vector in $\mathrm{xy}$ plane
(D) any unit vector in $\mathrm{xz}$ plane

Muhammad Nawaz

Numerade Educator

Problem 290

Find a unit vector in direction of $\hat{1}+2 \hat{\jmath}-3 \mathrm{k}$
(A) $(1 / \sqrt{7})(\hat{1}+2 \hat{\jmath}-3 \mathrm{k})$
(B) $-(1 / 2)(\hat{1}+2 \hat{\jmath}-3 \mathrm{k})$
(C) $(1 / \sqrt{14})(\hat{1}+2 \hat{j}-3 \mathrm{k})$
(D) $(1 / \sqrt{5})(\hat{1}+2 \hat{\jmath}-3 \mathrm{k})$

Muhammad Nawaz

Numerade Educator

Problem 291

Find a unit vector perpendicular to both $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$
(A) $\left[\left(\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}\right) / \mathrm{AB}\right]$
(B) $\left[\left(\mathrm{A}^{\rightarrow} \times \mathrm{B}^{-}\right) /(\mathrm{AB} \sin \theta)\right]$
(C) $\left[\left(\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right) /(\mathrm{AB} \cos \theta)\right]$
(D) $\left[\left(\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}\right) /(\mathrm{AB} \sin \theta)\right]$

Muhammad Nawaz

Numerade Educator

Problem 292

If resultant of $\mathrm{A}^{\rightarrow}=2 \hat{1}+\hat{\jmath}-\mathrm{k}^{\wedge}, \mathrm{B}^{\rightarrow}=\hat{\imath}-2 \hat{\mathrm{j}}+3 \mathrm{k}^{\text {and }} \mathrm{C}^{\rightarrow}$ is unit
vector in y direction, then $\mathrm{C}^{\rightarrow}$ is
(A) $-\hat{j}$
(B) $3 \hat{i}-2 \hat{j}+2 \mathrm{k}^{\wedge}$
(C)
(D) $2 \hat{i}+3 \mathrm{k}^{\wedge}$

Dheeraj Sharma

Numerade Educator

Problem 293

$\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ are two vectors $\mathrm{U}_{\mathrm{A}}^{\wedge}=\mathrm{U}_{\mathrm{B}}$ Now find the true
option.
(A) $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ equal vectors
(B) $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ are in opposite direction
(C) $\mathrm{A}^{\rightarrow}$ and $\mathrm{B}^{\rightarrow}$ are in same direction
(D) $\mathrm{A}^{\rightarrow} \perp \mathrm{B}^{\rightarrow}$

Muhammad Nawaz

Numerade Educator

Problem 294

Unit vector in direction of $\mathrm{A}^{\rightarrow}$ is
(A) $\left|\mathrm{A}^{\rightarrow}\right|$
(B) $\left[\mathrm{A}^{-} /\left(\left|\mathrm{A}^{-}\right|\right)\right]$
(C) $\left|\mathrm{A}^{-}\right| \mathrm{A}^{-}$
(D) $\left[\left(\left|\mathrm{A}^{-}\right|\right) / \mathrm{A}^{-}\right]$

Muhammad Nawaz

Numerade Educator

Problem 295

$(2 / 3) \hat{1}+(2 / 3) \hat{\jmath}+\mathrm{pk}$ is a unit vector so $\mathrm{p}=\ldots \ldots$
(A) $(2 / 3)$
(B) $-(1 / 3)$
(C) 1
(D) $(1 / 9)$

Muhammad Nawaz

Numerade Educator

Problem 296

Find a unit vector from the followings.
(A) $\hat{\imath}+\hat{j}$
(B) $\hat{\imath}-\hat{j}$
(C) $(1 / \sqrt{2}) \hat{\imath}+(1 / \sqrt{2}) \hat{\jmath}$
(D) $(1 / \sqrt{2}) \hat{1}-(1 / 2) \hat{\jmath}$

Muhammad Nawaz

Numerade Educator

Problem 297

Train $A$ is $56 \mathrm{~m}$ long and train $\mathrm{B} 54 \mathrm{~m}$ long. They are travelling in opposite direction with velocity $15(\mathrm{~m} / \mathrm{s})$ and $5(\mathrm{~m} / \mathrm{s})$ respectively. The time of crossing is.
(A) $12 \mathrm{~s}$
(B) $6 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $18 \mathrm{~s}$

Muhammad Nawaz

Numerade Educator

Problem 298

Graphs of velocity $\rightarrow$ time for two cars $\mathrm{A}$ and $\mathrm{B}$ moving in a straight line are given in the fig. The area covered by PQRS gives.
(A) distance from $\mathrm{A}$ to $\mathrm{B}$ at time $\mathrm{t}_{2}$
(B) distance from $\mathrm{A}$ to $\mathrm{B}$ at time $\mathrm{t}_{1}$
(C) distance from $\mathrm{A}$ to $\mathrm{B}$ in time interval $\mathrm{t}_{2}-\mathrm{t}_{1}$
(D) change in distance from $A$ to $B$ in time interval $t_{2}-t_{1}$

Vysakh M

Numerade Educator

Problem 299

Graphs velocity $\rightarrow$ time is given for cars $\mathrm{A}$ and $\mathrm{B}$ moving in a straight line in same direction. At time $t=0$ they are moving in the direction from $\mathrm{A}$ to $\mathrm{B}$, then.
(A) They will meet once
(B) They will never meet
(C) They will meet twice
(D) none of above is true

Vysakh M

Numerade Educator

Problem 300

Velocity of particle $\mathrm{A}$ with respect to particle $\mathrm{B}$ is $4(\mathrm{~m} / \mathrm{s})$ while they are moving in same direction. And it is $10(\mathrm{~m} / \mathrm{s})$ while they are in opposite direction. What are the velocities of the particles with respect to the stationary frame of reference.
(A) $7 \mathrm{~ms}^{-1}, 3 \mathrm{~ms}^{-1}$
(B) $4 \mathrm{~ms}^{-1}, 5 \mathrm{~ms}^{-1}$
(C) $7 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}$
(D) $10 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 301

Stone $\mathrm{A}$ is thrown in horizontal direction with velocity of $10 \mathrm{~ms}^{-1}$ at the same time stone $\mathrm{B}$ freely falls vertically in downward direction. Calculate the velocity of $\mathrm{B}$ with respect to $\mathrm{A}$ after 10 second.
(A) $10 \mathrm{~ms}^{-1}$
(B) $\sqrt{(101)} \mathrm{ms}^{-1}$
(C) $10 \sqrt{(101)} \mathrm{ms}^{-1}$
(D) 0

Muhammad Nawaz

Numerade Educator

Problem 302

A car moves horizontally with a speed of $3 \mathrm{~ms}^{-1}$. A glass wind screen is kept on the front side of the car. Rain drops strike the screen vertically. With the Velocity of $5 \mathrm{~ms}^{-1}$ Calculate the velocity of rain drops with respect to a ground.
(A) $6 \mathrm{~ms}^{-1}$
(B) $4 \mathrm{~ms}^{-1}$
(C) $3 \mathrm{~ms}^{-1}$
(D) $1 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 303

A man crosses a river through shortest distance D as given in the figure. $\mathrm{V}^{\rightarrow} \mathrm{R}$ is velocity of water and $\mathrm{V}^{\rightarrow} \mathrm{m}$ is velocity of
man in still river water. If $\mathrm{V}^{-} \mathrm{mR}$ is relative velocity of man
w. r. t. river, then find the angle made by swimming man with the shortest distance $\mathrm{AB}$
(A) $\tan ^{-1}\left[\mathrm{~V}_{\mathrm{R}} /\left(\mathrm{V}_{\mathrm{m}}-\mathrm{V}_{\mathrm{R}}\right)\right]$
(B) $\tan ^{-1}\left[\mathrm{~V}_{\mathrm{m}} / \sqrt{ \left.\left(\mathrm{V}_{\mathrm{R}}^{2}-\mathrm{V}_{\mathrm{m}}^{2}\right)\right]}\right.$
(C) $\tan ^{-1}\left[\mathrm{~V}_{\mathrm{R}} / \sqrt{ \left.\left(\mathrm{V}_{\mathrm{m}}^{2}-\mathrm{V}_{\mathrm{R}}^{2}\right)\right]}\right.$
(D) $\tan ^{-1}\left[\mathrm{~V}_{\mathrm{R}} / \sqrt{ \left.\left(\mathrm{V}_{\mathrm{R}}^{2}-\mathrm{V}_{\mathrm{m}}^{2}\right)\right]}\right.$

Nidhi Singhi

Numerade Educator

Problem 304

A particle has initial velocity $(2 \hat{1}+3 \hat{j}) \mathrm{ms}^{-1}$ and has acceleration $(\hat{1}+\hat{j}) \mathrm{ms}^{-2}$. Find the velocity of the particle after 2 second.
(A) $(3 \hat{1}+5 \hat{j}) \mathrm{ms}^{-1}$
(B) $(4 \hat{i}+5 \hat{\jmath}) \mathrm{ms}^{-1}$
(C) $(3 \hat{1}+2 \hat{j}) \mathrm{ms}^{-1}$
(D) $(5 \hat{1}+4 \hat{j}) \mathrm{ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 305

Motion of a body in $\mathrm{x}-\mathrm{y}$ plane is described by $\mathrm{r}^{\rightarrow}=\left[2 \mathrm{t} \hat{1}+\left(5 \mathrm{t}^{2}+6 \mathrm{t}\right) \hat{j}\right] \mathrm{m}$ Then find velocity of the body at
$\mathrm{t}=1$ second.
(A) $\sqrt{(144) \mathrm{ms}^{-1}}$
(B) $\sqrt{(148) \mathrm{ms}^{-1}}$
(C) $\sqrt{(150) \mathrm{ms}^{-1}}$
(D) $\sqrt{(260) \mathrm{ms}^{-1}}$

Muhammad Nawaz

Numerade Educator

Problem 306

A particle moves in $\mathrm{x}-\mathrm{y}$ plane. The position vector of the particle is given by $\mathrm{r}^{\rightarrow}=\left[3 \mathrm{ti}-2 \mathrm{t}^{2} \hat{\mathrm{j}}\right] \mathrm{m}$ Find the rate of change
of $\theta$ at $t=1$ second. Where $\theta$ is the angle between direction of motion and $x$
(A) $(16 / 25)$
(B) $(12 / 25)$
(C) $-(12 / 25)$
(D) $(16 / 9)$

Muhammad Nawaz

Numerade Educator

Problem 307

$x$ and y co-ordinates of a particle moving in $\mathrm{x}-\mathrm{y}$ plane at some instant are $\mathrm{x}=2 \mathrm{t}^{2}$ and $\mathrm{y}=(3 / 2) \mathrm{t}^{2}$ Calculate y co-ordinate when its $\mathrm{x}$ coordinate is $8 \mathrm{~m}$.
(A) $3 \mathrm{~m}$
(B) $6 \mathrm{~m}$
(C) $8 \mathrm{~m}$
(D) $9 \mathrm{~m}$

Muhammad Nawaz

Numerade Educator

Problem 308

A particle in $\mathrm{xy}$ plane is governed by $\mathrm{x}=\mathrm{A} \cos \omega \mathrm{t}, \mathrm{y}=\mathrm{A}$
$(1-\sin \omega \mathrm{t}) . \mathrm{A}$ and $\omega$ are constants. What is the speed of the particle.
(A) A\omegat
(B) $\mathrm{A} \omega^{2} \mathrm{t}$
(C) $\mathrm{A} \omega$
(D) $\mathrm{A}^{2} \omega \sin (\omega \mathrm{t} / 2)$

Muhammad Nawaz

Numerade Educator

Problem 309

A particle is moving in a xy plane with $\mathrm{y}=2 \mathrm{x}$ and $\mathrm{Vx}=2-\mathrm{t}$. Find $\mathrm{Vy}$ at time $\mathrm{t}=3$ second.
(A) $2 \mathrm{~ms}^{-1}$
(B) $-3 \mathrm{~ms}^{-1}$
(C) $+3 \mathrm{~ms}^{-1}$
(D) $-2 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 310

$\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ are two values of time of a projectile at the same height $t \mathrm{t}_{1}+\mathrm{t}_{2}=$
(A) Time to reach maximum height
(B) flight time for the projectile
(C) $(3 / 4)$ time of the flight time.
(D) $(3 / 2)$ time of the flight time.

Dheeraj Sharma

Numerade Educator

Problem 311

Equation of a projectile is given by $\mathrm{y}=\mathrm{Ax}-\mathrm{Bx}^{2}$. Find the range for the particle.
(A) $(\mathrm{A} / \mathrm{B})$
(B) $(\mathrm{A} / 4 \mathrm{~B})$
(C) $(\mathrm{A} / 2 \mathrm{~B})$
(D) $(2 \mathrm{~A} / \mathrm{B})$

Muhammad Nawaz

Numerade Educator

Problem 312

Angle of projection of a projectile with horizontal line is $\theta$ at time $t=0$, After what time the angle will be again $\theta$ ?
(A) $[(\mathrm{V} \cos \theta) / \mathrm{g}]$
(B) $[(\mathrm{V} \sin \theta) / \mathrm{g}]$
(C) $\left[\left(\mathrm{V}_{0} \sin \theta\right) / 2 \mathrm{~g}\right]$
(D) $\left[\left(2 \mathrm{~V}_{0} \sin \theta\right) / \mathrm{g}\right]$

Hast Aggarwal

Numerade Educator

Problem 313

A particle is projected with initial speed of $\mathrm{V}_{0}$ and angle of $\theta$. Find the horizontal displacement when its velocity is perpendicular to initial velocity.
(A) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\operatorname{gtan} \theta)\right]$
(B) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\mathrm{g} \sin \theta)\right]$
(C) $\left[\left(\mathrm{V}_{0} \sin \theta\right) / \mathrm{g}\right]$
(D) $\left[\left(\mathrm{V}_{0}^{2}\right) /(\tan \theta)\right]$

Satpal Satpal

Numerade Educator

Problem 314

Initial angle of a projectile is $\theta$ and its initial velocity is $\mathrm{V}_{0}$. Find the angle of velocity with horizontal line at time $\mathrm{t}$.
(A) $\sin ^{-1}\left[1-\left\{g /\left(\mathrm{V}_{0} \cos \theta\right)\right\} \mathrm{t}\right]$
(B) $\tan ^{-1}\left[1-\left\{g /\left(\mathrm{V}_{0} \cos \theta\right)\right\} \mathrm{t}\right]$
(C) $\tan ^{-1}\left[\tan \theta-\left\{g /\left(\mathrm{V}_{0} \cos \theta\right)\right\} \mathrm{t}\right]$
(D) $\sin ^{-1}\left[\tan \theta-\left\{g /\left(\mathrm{V}_{0} \cos \theta\right)\right\} \mathrm{t}\right]$

Prem Bijarniya

Numerade Educator

Problem 315

A stone is projected with an angle $\theta$ and velocity $\mathrm{V}_{0}$ from point $P$. It strikes the ground at point $Q$. If the both $P$ and $Q$ are on same horizontal line, then find average velocity.
(A) $V_{0} \cos \theta$
(B) $\mathrm{V}_{0} \sin \theta$
(C) $\mathrm{V}_{0} \cos (\theta / 2)$
(D) $\mathrm{V}_{0} \sin (\theta / 2)$

Hast Aggarwal

Numerade Educator

Problem 316

An object is projected with initial velocity of $100 \mathrm{~ms}^{-1}$ and angle of 60 . Find the vertical velocity when its horizontal displacement is $500 \mathrm{~m} .\left(\mathrm{g}=10 \mathrm{~ms}^{-1}\right)$
(A) $13.35 \mathrm{~ms}^{-1}$
(B) $-13.35 \mathrm{~ms}^{-1}$
(C) $-8.65 \mathrm{~ms}^{-1}$
(D) $98 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 317

Angle of projection of a projectile is changed, keeping initial velocity constant. Find the rate of change of maximum height. Range of the projectile is $\mathrm{R}$.
(A) $(\mathrm{R} / 4)$
(B) $(\mathrm{R} / 3)$
(C) $(\mathrm{R} / 2)$
(D) $\mathrm{R}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 318

A cartasian equation of a projectile is given by $\mathrm{y}=2 \mathrm{x}-5 \mathrm{x}^{2}$ Calculate its initial velocity.
(A) $\sqrt{10 \mathrm{~ms}^{-1}}$
(B) $\sqrt{5 \mathrm{~ms}^{-1}}$
(C) $\sqrt{2} \mathrm{~ms}^{-1}$
(D) $4 \mathrm{~ms}^{-1}$

Muhammad Nawaz

Numerade Educator

Problem 319

A body travelling in a circle at constant speed.
(A) has a constant velocity
(B) is not accelerated
(C) has an outward radial acceleration
(D) has an inward radial acceleration

Muhammad Nawaz

Numerade Educator

Problem 320

The speed of a particle moving in a circle of radius $\mathrm{r}=4$ meter is $10 \mathrm{~ms}^{-1}$. What is its radial acceleration?
(A) $25 \mathrm{~ms}^{-1}$
(B) $20 \mathrm{~ms}^{-2}$
(C) $10 \mathrm{~ms}^{-2}$
(D) $15 \mathrm{~ms}^{-2}$

Muhammad Nawaz

Numerade Educator

Problem 321

If $\mathrm{f}$ is the frequency of a body moving in a circular path with constant speed. a is its centrifugal acceleration, so.
(A) $\mathrm{a} \propto \mathrm{f}$
(B) a $\propto \mathrm{f}^{2}$
(C) $\mathrm{a} \propto \mathrm{f}^{3}$
(D) a $\propto(1 / \mathrm{f})$

Muhammad Nawaz

Numerade Educator

Problem 322

Assertion:
(A) If both Assertion - Reason are true, reason is correct explanation of Assertion.
(B) If both Assertion - Reason are true but reason is not correct explanation of Assertion.
(C) Assertion is true but Reason is false.
(D) If Reason is true but Assertion is false
At the highest point of projectile motion the velocity is not zero. Reason: Only the vertical component of velocity is zero. Where as horizontal component still exists.
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

Vysakh M

Numerade Educator

Problem 323

Match column type question At any instant, the horizontal position to balloon is defined by $\mathrm{x}=\mathrm{gt} \mathrm{m} .$ Equation of path is $\left(\mathrm{x}^{2} / 30\right)$. After $\mathrm{t}=2 \mathrm{sec}$, match
the following.
Table 1 Table 2
(A) distance of balloon from station $\mathrm{A}$.
(P) $14.1,50^{\circ}$
(B) magnitude \& direction of velocity
(Q) $24 \mathrm{~m}$
C) magnitude \& direction of acceleration
(R) $21 \mathrm{~m}$
(S) $5.4,90^{\circ}$
(A) $\mathrm{A}-\mathrm{R}, \mathrm{B}-\mathrm{S}, \mathrm{C}-\mathrm{P}$
(B) $\mathrm{A}-\mathrm{Q}, \mathrm{B}-\mathrm{S}, \mathrm{C}-\mathrm{P}$
(C) $\mathrm{A}-\mathrm{R}, \mathrm{B}-\mathrm{P}, \mathrm{C}-\mathrm{S}$
(D) $\mathrm{A}-\mathrm{Q}, \mathrm{B}-\mathrm{P}, \mathrm{C}-\mathrm{S}$

Nidhi Singhi

Numerade Educator

Problem 324

Comprehensions type questions. A particle is moving in a circle of radius $\mathrm{R}$ with constant speed. The time period of the particle is T Now after time $\mathrm{t}=(\mathrm{T} / 6)$
Average speed of the particle is
(A) $(\pi \mathrm{R} / 6 \mathrm{~T})$
(B) $[(2 \pi R) / 3 \mathrm{~T}]$
(C) $[(2 \pi R) / T]$
(D) $(\mathrm{R} / \mathrm{T})$

Muhammad Nawaz

Numerade Educator

Problem 325

Comprehensions type questions. A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is T Now after time $\mathrm{t}=(\mathrm{T} / 6)$
Average velocity of the particle is
(A) $(3 \mathrm{R} / \mathrm{T})$
(B) $(6 \mathrm{R} / \mathrm{T})$
(C) $(2 \mathrm{R} / \mathrm{T})$
(D) $(4 \mathrm{R} / \mathrm{T})$

Muhammad Nawaz

Numerade Educator

Problem 326

Comprehensions type questions. A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $\mathrm{T}$ Now after time $\mathrm{t}=(\mathrm{T} / 6)$
Range of a projectile is $R$ and maximum height is $\mathrm{H}$. Find the area covered by the path of the projectile and horizontal line.
(A) $(2 / 3) \mathrm{RH}$
(B) $(5 / 3) \mathrm{RH}$
(C) $(3 / 5) \mathrm{RH}$
(D) $(6 / 5) \mathrm{RH}$

Muhammad Nawaz

Numerade Educator