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Master Resource Book in JEE Main Physics

D. B. Singh

Chapter 2

Kinematics - all with Video Answers

Educators

Section 1

Round 1

02:40

Problem 1

A wheel of radius $1 \mathrm{~m}$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is
(a) $2 \pi$
(b) $\sqrt{2} \pi$
(c) $\sqrt{\pi^{2}+4}$
(d) $\pi$

Mahendra Rathore
Mahendra Rathore
Numerade Educator
01:34

Problem 2

A point particle starting from rest has a velocity that increases linearly with time such that $v=p t$, where $p=4 \mathrm{~ms}^{-2}$. The distance covered in the first 2 s will be
(a) $6 \mathrm{~m}$
(b) $4 \mathrm{~m}$
(c) $8 \mathrm{~m}$
(d) $10 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
00:41

Problem 3

Among the four graphs, there is only one graph for which average velocity over the time intervel $(0, T)$ can vanish for a suitably chosen $T$. Which one is it?
(a)
(b)
(c)
(d)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:13

Problem 4

A particle moves with constant acceleration and $v_{1}, v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals $t_{1}, t_{2}$ and $t_{3}$ of time. Which of the following relations is correct?
(a) $\frac{v_{1}-v_{2}}{v_{2}-v_{3}}=\frac{t_{1}-t_{2}}{t_{2}+t_{3}}$
(b) $\frac{v_{1}-v_{2}}{v_{2}-v_{3}}=\frac{t_{1}-t_{2}}{t_{1}-t_{2}}$
(c) $\frac{v_{1}-v_{2}}{v_{2}-v_{3}}=\frac{t_{1}-t_{2}}{t_{2}-t_{3}}$
(d) $\frac{v_{1}-v_{2}}{v_{2}-v_{3}}=\frac{t_{1}+t_{2}}{t_{2}+t_{3}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:10

Problem 5

The displacement of a body along $x$-axis depends on time as $\sqrt{x}=t+1$. Then, the velocity of body
(a) increase with time
(b) decrease with time
(c) independent of time
(d) None of these

Akshaya Rs
Akshaya Rs
Numerade Educator
03:29

Problem 6

A car moving along a straight highway with speed of $126 \mathrm{~km} / \mathrm{h}$ is brought to a stop within a distance of $200 \mathrm{~m}$. What is the retardation of the car (assumed uniform) and how long does it take for the car to stop? [NCERT]
(a $3.06 \mathrm{~m} / \mathrm{s}^{2}$ and $11.4 \mathrm{~s}$
(b) $206 \mathrm{~m} / \mathrm{s}^{2}$ and $11.4 \mathrm{~s}$
(c) $3.06 \mathrm{~m} / \mathrm{s}^{2}$ and $10.4 \mathrm{~s}$
(d) $3.06 \mathrm{~m} / \mathrm{s}^{2}$ and $4.1 \mathrm{~s}$

Vipender Rao
Vipender Rao
Numerade Educator
02:13

Problem 7

A particle of mass $m$ is initially situated at the point $P$ inside a hemispherical surface of radius $r$ as shown in figure. A horizontal acceleration of magnitude $a_{0}$ is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, the time taken by particle to touch the sphere again is
(a) $\sqrt{\frac{4 r \sin \alpha}{a_{0}}}$
(b) $\sqrt{\frac{4 r \tan \alpha}{a_{0}}}$
(c) $\sqrt{\frac{4 r \cos \alpha}{a_{0}}}$
(d) None of these

Mahendra K
Mahendra K
Numerade Educator
01:53

Problem 8

A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the $n$th second to the distance covered in $n$ second is
(a) $\frac{2}{n}-\frac{1}{n^{2}}$
(b) $\frac{1}{n^{2}}-\frac{1}{n}$
(c) $\frac{2}{n^{2}}-\frac{1}{n}$
(d) $\frac{2}{n}+\frac{1}{n^{2}}$

Mahendra K
Mahendra K
Numerade Educator
03:59

Problem 9

A particle moving with a uniform acceleration along a straight line covers distance $a$ and $b$ in successive intervals of $p$ and $q$ second. The acceleration of the particle is
(a) $\frac{p q(p+q)}{2(b p-a q)}$
(b) $\frac{2(a q-b p)}{p q(p-q)}$
(c) $\frac{b p-a q}{p q(p-q)}$
(d) $\frac{2(b p-a q)}{p q(p-q)}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:52

Problem 10

42. A particle moves along $x$-axis as
$$
x=4(t-2)+a(t-2)^{2}
$$
Which of the following is true?
(a) The initial velocity of particle is 4
(b) The acceleration of particle is $2 \mathrm{a}$
(c) The particle is at origin at $t=0$
(d) None of the above

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:39

Problem 11

A $2 \mathrm{~m}$ wide truck is moving with a uniform speed $v_{0}=8 \mathrm{~ms}^{-1}$ along a straight horizontal road. $\mathrm{A}$ pedestrian starts to cross the road with a uniform speed $v$ when the truck is $4 \mathrm{~m}$ away from him. The minimum value of $v$, so that he can cross the road safely is $\begin{array}{ll}\text { (a) } 2.62 \mathrm{~ms}^{-1} & \text { (b) } 4.6 \mathrm{~ms}^{-1}\end{array}$
(c) $3.57 \mathrm{~ms}^{-1}$
(d) $1.414 \mathrm{~ms}^{-1}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:20

Problem 12

A bus moves over a straight level road with a constant acceleration $a .$ A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively
(a) $a$ and $g$
(b) $a+g$ and $g-a$
(c) $\sqrt{a^{2}+g^{2}}$ and $g$
(d) $\sqrt{a^{2}+g^{2}}$ and $a$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:09

Problem 13

Two cars move in the same direction along parallel roads. One of them is a $100 \mathrm{~m}$ long travelling with a velocity of $7.5 \mathrm{~ms}^{-1}$. How long will it take for the first car to overtake the second car? (a) $24 \mathrm{~s}$
(c) $40 \mathrm{~s}$
$\begin{array}{ll}\text { (c) } 60 \mathrm{~s} & \text { (d) } 80 \mathrm{~s}\end{array}$

Mahendra K
Mahendra K
Numerade Educator
01:16

Problem 14

A car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance with velocities $30 \mathrm{kmh}^{-1}$ and $40 \mathrm{kmh}^{-2}$ respectively. The velocity of car midway between $P$ and $Q$ is $\begin{array}{ll}\text { (a) } 33.3 \mathrm{~km}^{-1} & \text { (b) } 1 \mathrm{~km}^{-1}\end{array}$
$\begin{array}{ll}\text { (c) } 25 \sqrt{2} \mathrm{~km}^{-1} & \text { (d) } 35.35 \mathrm{~km}^{-1}\end{array}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:12

Problem 15

A particle starts from the origin and moves along the $X$-axis such that the velocity at any instant is given by $4 t^{3}-2 t$, where $t$ is in second and velocity is in $\mathrm{ms}^{-1} .$ What is the acceleration of the particle when it is $2 \mathrm{~m}$ from the origin? (a) $10 \mathrm{~ms}^{-2}$
(b) $12 \mathrm{~ms}^{-2}$
(c) $22 \mathrm{~ms}^{-2}$
(d) $28 \mathrm{~ms}^{-2}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:14

Problem 16

The retardation experienced by a moving motor boat, after its engine is cut-off, is given by $\frac{d v}{d t}=-k v^{3}$, where $k$ is a constant. If $v_{0}$ is the magnitude of the velocity at cut-off, the magnitude of the velocity at time $t$ after the cut-off is
(a) $v_{0}$
(b) $\frac{v_{0}}{2}$
(c) $v_{0} e^{-k t}$
(d) $\frac{v_{0}}{\sqrt{2 v_{0}^{2} k t+1}}$

Nishant Kumar
Nishant Kumar
Numerade Educator
01:10

Problem 17

The driver of a car moving with a speed of $10 \mathrm{~ms}^{-1}$ sees a red light ahead, applies brakes and stops after covering $10 \mathrm{~m}$ distance. If the same car were moving with a speed of $20 \mathrm{~ms}^{-1}$, the same driver would have stopped the car after covering $30 \mathrm{~m}$ distance. Within what distance the car can be stopped if travelling with a velocity of $15 \mathrm{~ms}^{-1}$ ? Assume the same reaction time and the same deceleration in each case.
(a) $18.75 \mathrm{~m}$
(b) $20.75 \mathrm{~m}$
(c) $22.75 \mathrm{~m}$
(d) $25 \mathrm{~m}$

Shoukat Ali
Shoukat Ali
Other Schools
01:16

Problem 18

A lift is coming from $8^{\text {th }}$ floor and is just about to reach $4^{\text {th }}$ floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct? [NCERT Exemplar]
(a) $x<0, v<0, a>0$
(b) $x>0, v<0, a<0$
(c) $x>0, v<0, a>0$
(d) $x>0, v>0, a<0$

Supratim Pal
Supratim Pal
Numerade Educator
07:06

Problem 19

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4 \mathrm{~cm}$ and that of iron plate is $2 \mathrm{~cm}$. A bullet fired goes through the wood first and then penetrates $1 \mathrm{~cm}$ into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates $2 \mathrm{~cm}$ into wood. If $a_{1}$ and $a_{2}$ be the retardation offered to the bullet by wood and iron plates respectively, then
(a) $t_{1}+t_{2}$
(b) $a_{2}=2 a_{1}$
(c) $a_{1}=a_{2}$
(d) data insufficient

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:49

Problem 20

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \mathrm{~ms}^{-1}$ to a value approaching zero at $s=30 \mathrm{~m}$, then acceleration of the particle at $s=15 \mathrm{~m}$ is
(a) $\frac{2}{3} \mathrm{~ms}^{-2}$
(b) $-\frac{2}{3} \mathrm{~ms}^{-2}$
(c) $\frac{20}{3} \mathrm{~ms}^{-2}$
(d) $-\frac{20}{3} \mathrm{~ms}^{-2}$

Ajay Singhal
Ajay Singhal
Numerade Educator
02:35

Problem 21

The velocity of a particle moving in a straight line varies with time in such a manner that $v$ versus $t$ graph is velocity is $v_{m}$ and the total time of motion is $t_{0}$
(i) Average velocity of the particle is $\frac{\pi}{4} v_{m}$
(ii) Such motion cannot be realized in practical terms
(a) Only (i) is correct
(b) Only (ii) is correct
(c) Both (i) and (ii) are correct
(d) Both (i) and (ii) are wrong

Mahendra Rathore
Mahendra Rathore
Numerade Educator
01:53

Problem 22

A police van moving on a highway with a speed of $30 \mathrm{~km} / \mathrm{h}$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192 \mathrm{~km} / \mathrm{h}$. If the muzzle speed of the bullet is $150 \mathrm{~m} / \mathrm{s}$, with what speed does the bullet hit the thief's car? (Note Obtain that speed which is relevant for damaging the thiefs car. [NCERT]
(a) $105 \mathrm{~m} / \mathrm{s}$
(b) $100 \mathrm{~m} / \mathrm{s}$
(c) $95 \mathrm{~m} / \mathrm{s}$
(d) $110 \mathrm{~m} / \mathrm{s}$

Akshaya Rs
Akshaya Rs
Numerade Educator
03:08

Problem 23

A particle starts from rest and travels a distance $s$ with uniform acceleration, then it travels a distance $2 s$ with uniform speed, finally it travels a distance $3 s$ with uniform retardation and comes to rest. If the complete motion of the particle in a straight line then the ratio of its average velocity to maximum velocity in
(a) $6 / 7$
(b) $4 / 5$
(c) $3 / 5$
(d) $2 / 5$

Akshaya Rs
Akshaya Rs
Numerade Educator
03:59

Problem 24

A particle moving in a straight line with uniform acceleration is observed to be a distance $a$ from a fixed point initially. It is at distances $b, c, d$ from the same point after $n, 2 n, 3 n$ second. The acceleration of the particle is
(a) $\frac{c-2 b+a}{n^{2}}$
(b) $\frac{c+b+a}{9 n^{2}}$
(c) $\frac{c+2 b+a}{4 n^{2}}$
(d) $\frac{c-b+a}{n^{2}}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:24

Problem 25

A body is moving along a straight line path with constant velocity. At an instant of time the distance of time the distance travelled by it is $s$ and its displacement is $D$, then
(a) $D<s$
(b) $D>5$
(c) $D=s$
(d) $D \leq s$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:47

Problem 26

Three particles start from the origin at the same time, one with a velocity $v_{1}$ along $x$-axis, the second along the $y$-axis with a velocity $v_{2}$ and the third along $x=y$ line. The velocity of the third so that the three may always lie on the same line is
(a) $\frac{v_{1} v_{2}}{v_{1}+v_{2}}$
(b) $\frac{\sqrt{2} v_{1} v_{2}}{v_{1}+v_{2}}$
(c) $\frac{\sqrt{3} v_{1} v_{2}}{v_{1}+v_{2}}$
(d) zero

Vishal Gupta
Vishal Gupta
Numerade Educator
02:02

Problem 27

In one dimensional motion, instantaneous speed $v$ satisfies $0 \leq v<v_{0}$
[NCERT Exemplar]
(a) The displacement in time $T$ must always take non-negative values
(b) The displacement $x$ in time $T$ satisfies $-v_{0} T<x<v_{0} T$
(c) The acceleration is always a non-negative number
(d) The motion has no turning points

Supratim Pal
Supratim Pal
Numerade Educator
02:45

Problem 28

The engine of a train can impart a maximum acceleration of $1 \mathrm{~ms}^{-2}$ and the brakes can give a maximum retardation of $3 \mathrm{~ms}^{-2} .$ The least time during which a train can go from one place to the other place at a distance of $1.2 \mathrm{~km}$ is nearly
(a) $108 \leq$
(b) $191 \mathrm{~s}$
(c) $56.6 \mathrm{~s}$
(d) time is fixed

Satpal Satpal
Satpal Satpal
Numerade Educator
02:00

Problem 29

The acceleration of a particle increasing linearly with time $t$ is $b t$. The particle starts from the origin with an initial velocity $v_{0}$. The distance travelled by the particle in time $t$ will be
(a) $v_{0} t+\frac{1}{6} b t^{3}$
(b) $v_{0} t+\frac{1}{6} b t^{2}$
(c) $v_{0} t+\frac{1}{3} b t^{3}$
(d) $v_{0} t+\frac{1}{3} b t^{2}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:42

Problem 30

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point
(a) $C$
(b) $D$
(c) $E$
(d) $F$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 31

In the given $v-t$ graph, the distance travelled by the body in $5 \mathrm{~s}$ will be
(a) $20 \mathrm{~m}$
(b) $40 \mathrm{~m}$
(c) $80 \mathrm{~m}$
(d) $100 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
00:55

Problem 32

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the $x$-axis. The ratio of the two velocities is
(a) $\sqrt{3}: 1$
(b) $1: 1$
(c) $1: 2$
(d) $1: \sqrt{3}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
12:45

Problem 33

A rocket is fired upwards. Its engine explodes fully is 12 s. The height reached by the rocket as calculated from its velocity-time graph is
(a) $1200 \times 66 \mathrm{~m}$
(b) $1200 \times 132 \mathrm{~m}$
(c) $\frac{1200}{12} \mathrm{~m}$
(d) $1200 \times 12^{2} \mathrm{~m}$

MK
Michael Kretovic
Numerade Educator
02:09

Problem 34

$v-t$ graph for a particle is as shown. The distance travelled in the first $4 \mathrm{~s}$ is
(a) $12 \mathrm{~m}$
(b) $16 \mathrm{~m}$
(c) $20 \mathrm{~m}$
(d) $24 \mathrm{~m}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:05

Problem 35

The velocity-time graph of a body is shown in figure. The ratio of the ..... during the intervals $O A$ and $A B$ is .....
(a) average velocities: 2
(b) $\frac{O A}{A B}: \frac{1}{3}$
(c) average accelerations, same as distances covered
(d) distances covered : $\frac{1}{2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:47

Problem 36

Figure shows the acceleration-time graphs of a particle. Which of the following represents the corresponding velocity-time graphs?
(a)
(b)
(c)
(d)

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:03

Problem 37

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?
(a)
(b)
(c)
(d)

Akshaya Rs
Akshaya Rs
Numerade Educator
01:33

Problem 38

A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$. At time $t$, the speed of $A$ relative to $B$ is
(a) $y$
(b) $2 u$
(c) $u-g t$
(d) $\sqrt{\left(u^{2}-g t\right)}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:20

Problem 39

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of
(a) $3 \mathrm{~s}$
(b) $5 \mathrm{~s}$
(c) $7 \underline{5}$
(d) $9 \mathrm{~s}$

Nishant Kumar
Nishant Kumar
Numerade Educator
03:25

Problem 40

Rain is falling vertically with a speed of $30 \mathrm{~m} / \mathrm{s} . \mathrm{A}$ woman rides a bicycle with a speed of $10 \mathrm{~m} / \mathrm{s}$ in the north to south direction. What is the direction in which she should hold her umbrella? [NCERT]
(a) $18^{\circ}$ with vertical
(b) $18^{\circ}$ with horizontal
(c) $28^{\circ}$ with vertical
(d) $28^{\circ}$ with horizontal

Sanu Kumar
Sanu Kumar
Numerade Educator
04:33

Problem 41

A ball $P$ is dropped vertically and another ball $Q$ is thrown horizontally with the same velocities from the same height and at the same time. If air resistance is neglected, then
(a) ball $P$ reaches the ground first
(b) ball $Q$ reaches the ground first
(c) both reach the ground at the same time
(d) the respective masses of the two balls will decide the time

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:52

Problem 42

A particle moves along $x$-axis as
$$
x=4(t-2)+a(t-2)^{2}
$$
Which of the following is true?
(a) The initial velocity of particle is 4
(b) The acceleration of particle is $2 \mathrm{a}$
(c) The particle is at origin at $t=0$
(d) None of the above

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:17

Problem 43

A ball is thrown vertically upwards. It was observed at a height $h$ twice with a time a interval $\Delta t$ the initial velocity of the ball is
(a)
(b)
(c) $1 / 2 \sqrt{8 g h+g^{2}(\Delta t)^{2}}$
(d) $\sqrt{8 g h+4 g^{2}(\Delta t)^{2}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:25

Problem 44

A frictionless wire $A B$ is fixed on a sphere of radius $R$. A very small spherical ball slips on this wire the time taken by this ball to slip from $A$ to $B$ is
(a) $\frac{2 \sqrt{g R}}{g \cos \theta}$
(b) $2 \sqrt{g R} \frac{\cos \theta}{g}$
(c) $2 \sqrt{\frac{R}{g}}$
(d) $\frac{g R}{\sqrt{g \cos \theta}}$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:47

Problem 45

A jet airplane travelling at a speed of $500 \mathrm{~km} / \mathrm{h}$ ejects its products of combustion at the speed of $1500 \mathrm{~km} / \mathrm{h}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground? [NCERT]
(a) $-1000 \mathrm{~km} / \mathrm{h}$
(b) $1000 \mathrm{~km} / \mathrm{h}$
(c) $100 \mathrm{~km} / \mathrm{h}$
(d) $-100 \mathrm{~km} / \mathrm{h}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:52

Problem 46

A body is thrown vertically up with a velocity $u$. It passes three points $A, B$ and $C$ in its upward journey with velocities $\frac{u}{2}, \frac{u}{3}$ and $\frac{u}{4}$ repectively. The ratio of the separations between points $A$ and $B$ and between $B$ and $C$, i.e.,$\frac{A B}{B C}$ is
$\begin{array}{llll}\text { (a) } 1 & \text { (b) } 2 & \text { (c) } \frac{10}{7} & \text { (d) } \frac{20}{7}\end{array}$

Satpal Satpal
Satpal Satpal
Numerade Educator
06:58

Problem 47

A boy released a ball from the top of a building. It will clear a window $2 \mathrm{~m}$ high at a distance $10 \mathrm{~m}$ below the top in nearly
(a) $1 \mathrm{~s}$
(b) $1.3 \mathrm{~s}$
(c) $0.6 \mathrm{~s}$
(d) $0.13 \mathrm{~s}$

Darren Wilson
Darren Wilson
Numerade Educator
02:00

Problem 48

A stone is allowed to fall from the top of a tower $100 \mathrm{~m}$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $254 \mathrm{~ms}^{-1}$. The two stones will meet after
$\begin{array}{llll}\text { (a) } 4 \mathrm{~s} & \text { (b) } 0.4 \mathrm{~s} & \text { (c) } 0.04 \mathrm{~s} & \text { (d) } 40 \mathrm{~s}\end{array}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:35

Problem 49

From a balloon rising vertically upwards at $5 \mathrm{~m} / \mathrm{s}$ a stone is thrown up at $10 \mathrm{~m} / \mathrm{s}$ relative to the balloon. Its velocity with respect to ground after $2 \mathrm{~s}$ is (assume $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $\underline{0}$
(b) $20 \mathrm{~m} / \mathrm{s}$
(c) $10 \mathrm{~m} / \mathrm{s}$
(d) $5 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:20

Problem 50

A body thrown vertically upward with an initial velocity $u$ reaches maximum height in 6 second. The ratio of the distances travelled by the body in the first second and seventh second is
(a) $1: 1$
(b) $11: 1 \quad$ (c) $1: 2$
(d) $1: 11$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:54

Problem 51

A juggler keeps on moving four balls in the air throws the balls in regular interval of time. When one ball leaves his hand (speed $=20 \mathrm{~ms}^{-1}$ ), the position of other ball will be (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $10 \mathrm{~m}, 20 \mathrm{~m}, 10 \mathrm{~m}$
(b) $15 \mathrm{~m}, 20 \mathrm{~m}, 15 \mathrm{~m}$
(c) $5 \mathrm{~m}, 15 \mathrm{~m}, 20 \mathrm{~m}$
(d) $5 \mathrm{~m}, 10 \mathrm{~m}, 20 \mathrm{~m}$

Mahendra K
Mahendra K
Numerade Educator
03:44

Problem 52

The velocity-time graph of a particle in one-dimensional motion is shown in figure. Which of the following formulae are correct for describing the motion of the particle over the time interval $t_{1}$ to $t_{2}$.
(i) $x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\frac{1}{2} a\left(t_{2}-t_{1}\right)^{2}$
(ii) $v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right)$
(iii) $v_{a v}=\left[\frac{x\left(t_{2}\right)-x\left(t_{1}\right)}{\left(t_{2}-t_{1}\right)}\right]$
(iv) $a_{\mathrm{av}}=\frac{\left[v\left(t_{2}\right)-v\left(t_{1}\right)\right]}{\left(t_{2}-t_{1}\right)}$
(v) $x\left(t_{2}\right)=x\left(t_{1}\right)+v_{\mathrm{av}}\left(t_{2}-t_{1}\right)+\frac{1}{2} a_{\mathrm{av}}\left(t_{2}-t_{1}\right)^{2}$
(vi) $x\left(t_{2}\right)-x\left(t_{1}\right)=$ Area under $v-t$ curve bounded by the $t$-axis and the dotted line shown
(a) (iii) and (vi)
(b) (iii), (iv) and (vi)
(c) (ii), (iii) and (iv)
(d) (iv) and (vi)

Vipender Rao
Vipender Rao
Numerade Educator
02:21

Problem 53

Water drops fall from a tap on the floor $5 \mathrm{~m}$ below at regular intervals of time, the first drop striking the floor when the fifth drop begins to fall. The height at which the third drop will be, from ground, at the instant when first drop strikes the ground, will be $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $1.25 \mathrm{~m}$
(b) $2.15 \mathrm{~m}$
(c) $2.73 \mathrm{~m}$
(d) $3.75 \mathrm{~m}$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:00

Problem 54

From an elevated point $A$, a stone is projected vertically upwards. When the stone reaches a distance $h$ below $A$, its velocity is double of what was at a height above $A$ ? The greatest height attained by the stone is
(a) $\frac{h}{3}$
(b) $\frac{2 h}{2}$
(c) $\frac{h}{2}$
(d) $\frac{5 h}{3}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:33

Problem 55

A ball is thrown vertically upwards from the top of a tower of height $h$ with velocity $v$. The ball strikes the ground after
$$
\begin{array}{ll}
\text { (a) } \frac{v}{g}\left[1+\sqrt{1+\frac{2 g h}{v^{2}}}\right] & \text { (b) } \frac{v}{g}\left[1+\sqrt{1-\frac{2 g h}{v^{2}}}\right] \\
\text { (c) } \frac{v}{g}\left(1+\frac{2 g h}{v^{2}}\right)^{1 / 2} & \text { (d) } \frac{v}{g}\left(1-\frac{2 g h}{v^{2}}\right)^{1 / 2}
\end{array}
$$

Akshaya Rs
Akshaya Rs
Numerade Educator
02:05

Problem 56

A body freely falling from rest has a velocity $v$ after it falls through distance $h .$ The distance it has to fall down further for its velocity to become double is
(a) $h$
(b) $2 \mathrm{~h}$
(c) $3 h$
(d) $4 h$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
04:33

Problem 57

Two balls $A$ and $B$ are thrown simultaneously from the top of a tower. $A$ is thrown vertically up with a speed of $4 \mathrm{~ms}^{-1} . B$ is thrown vertically down with a speed of $4 \mathrm{~ms}^{-1}$. The ball $A$ and $B$ hit the ground with speed $v_{A}$ and $v_{B}$ respectively. Then, $\begin{array}{llll}\text { (a) } v_{A}<v_{B} & \text { (b) } v_{A}>v_{B} & \text { (c) } v_{A} \geq v_{B} & \text { (d) } v_{A}=v_{B}\end{array}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:50

Problem 58

A particle starting from rest falls from a certain height. Assuming that the value of acceleration due to gravity remains the same throughout motion, its displacements in three successive half second intervals are $S_{1}, S_{2}, S_{3} .$ Then, (a) $S_{1}: S_{2}: S_{3}=1: 5: 9 \quad$ (b) $S_{1}: S_{2}: S_{3}=1: 2: 3$
(c) $S_{1}: S_{2}: S_{3}=1: 1: 1$
(d) $S_{1}: S_{2}: S_{3}=1: 3: 5$

Muhammad Nawaz
Muhammad Nawaz
Numerade Educator
04:46

Problem 59

A ball thrown upward from the top of a tower with speed $v$ reaches the ground in $t_{1}$ second. If this ball is thrown downward from the top of the same tower with speed $v$ it reaches the ground in $t_{2}$ second. In what time the ball shall reach the ground if it is allowed to falls freely under gravity from the top of the tower? $\begin{array}{lll}\text { (a) } \frac{t_{1}+t_{2}}{2} & \text { (b) } \frac{t_{1}-t_{2}}{2} & \text { (c) } \sqrt{t_{1} t_{2}}\end{array}$
(d) $t_{1}+t_{2}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:45

Problem 60

A ball is dropped on the floor from a height of $10 \mathrm{~m}$. It rebounds to a height of $2.5 \mathrm{~m}$. If the ball is in contact with the floor for $0.01 \mathrm{~s}$, the average acceleration during contact is nearly (Take $g=10 \mathrm{~ms}^{-2}$ ) $\begin{array}{ll}\text { (a) } 500 \sqrt{2} \mathrm{~ms}^{-2} \text { upwards } & \text { (b) } 1800 \mathrm{~ms}^{-2} \text { downwards }\end{array}$
$\begin{array}{ll}\text { (c) } 1500 \sqrt{5} \mathrm{~ms}^{-2} \text { upwards } & \text { (d) } 1500 \sqrt{2} \mathrm{~ms}^{-2} \text { downwards }\end{array}$

Vysakh M
Vysakh M
Numerade Educator
01:46

Problem 61

A stone thrown vertically upwards attains a maximum height of $45 \mathrm{~m} .$ In what time the velocity of stone become equal to one-half the velocity of throw? (Given $g=10 \mathrm{~ms}^{-2}$ )
(a) $2 \mathrm{~s}$
(b) $1.5 \mathrm{~s}$
(c) $1 \mathrm{~s}$
(d) $0.5 \mathrm{~s}$

Supratim Pal
Supratim Pal
Numerade Educator
02:53

Problem 62

A body released from a great height falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies two second after the release of the second body is
$\begin{array}{lll}\text { (a) } 9.8 \mathrm{~m} & \text { (b) } 4.9 \mathrm{~m} & \text { (c) } 24.5 \mathrm{~m}\end{array}$
(d) $19.6 \mathrm{~m}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:19

Problem 63

A particle covers $4 \mathrm{~m}, 5 \mathrm{~m}, 6 \mathrm{~m}$ and $7 \mathrm{~m}$ in $3 \mathrm{rd}, 4$ th, 5th and 6th second respectively. The particle starts
(a) with an initial non-zero velcoity and moves with uniform acceleration
(b) from rest and moves with uniform velocity
(c) with an initial velocity and moves with uniform velcoity
(d) from rest and moves with uniform acceleration

Supratim Pal
Supratim Pal
Numerade Educator
03:03

Problem 64

A balls is released from the top of a tower travels $\frac{11}{36}$ of
the height of the tower in the last second of its journey. The height of the tower is (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $11 \mathrm{~m}$
(b) $36 \mathrm{~m}$
(c) $47 \mathrm{~m}$
(d) $180 \mathrm{~m}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
03:37

Problem 65

At a metro station, a girl walks up a stationary escalator in time $t_{1}$. If she remains stationary on the escalator, then the escalator take her up in time $t_{2}$. The time taken by her to walk up on the moving escalator will be [NCERT Exemplar]
(a) $\left(t_{1}+t_{2}\right) / 2$
(b) $t_{1} t_{2} /\left(t_{2}-t_{1}\right)$
(c) $t_{1} t_{2} /\left(t_{2}+t_{1}\right)$
(d) $t_{1}-t_{2}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
07:23

Problem 66

A $120 \mathrm{~m}$ long train is moving in a direction with speed $20 \mathrm{~m} / \mathrm{s}$. A train $B$ moving with $30 \mathrm{~m} / \mathrm{s}$ in the opposite direction and $130 \mathrm{~m}$ long crosses the first train in a time.
(a) $6 \mathrm{~s}$
(b) $36 \mathrm{~s}$
(c) $38 \mathrm{~s}$
(d) None of these

Subash Charan
Subash Charan
Numerade Educator
02:08

Problem 67

For a body moving with relative speed of the velocity is doubled, then
(a) its linear momentum is doubled
(b) its linear momentum will be less than doubled
(c) its linear momentum will be more than doubled
(d) its linear momentum remains unchanged

Vysakh M
Vysakh M
Numerade Educator
01:42

Problem 68

An express train is moving with a velocity $v_{1}$ its driver finds another train is moving on the same track in the same direction with velocity $v_{2}$. To avoid collision driver applies a retardation $a$ on the train. The minimum time of avoiding collision will be
(a) $t=\frac{v_{1}-v_{2}}{a}$
(b) $t=\frac{v_{1}^{2}-v_{2}^{2}}{2}$
(c) None
(d) Both (a) and (b)

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:00

Problem 69

Rain drops fall vertically at a speed of $20 \mathrm{~ms}^{-1}$. At what angle do they fall on the wind screen of a car moving with a velocity of $15 \mathrm{~ms}^{-1}$, if the wind screen velocity inclined at an angle of $23^{\circ}$ to the vertical? $\left[\cot ^{-1}\left(\frac{4}{3}\right)=36^{\circ}\right]$
(a) $60^{\circ}$
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $90^{\circ}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:51

Problem 70

A man wants to reach point $B$ on the opposite bank of river flowing at a speed shown in figure. What minimum speed relative water should the man have so that he can reach point $\begin{array}{llll}\text { (a) } u \sqrt{2} & \text { (b) } u / \sqrt{2} & \text { (c) } 2 u & \text { (d) } u\end{array}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:53

Problem 71

A steam boat goes across a lake and comes back (i) on a quiet day when the water is still and (ii) on a rough day when there is a uniform current so as to help the journey onwards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be
(a) more
(b) less
(c) same
(d) None of these

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:30

Problem 72

Two trains travelling on the same track are approaching each other with equal speeds of $40 \mathrm{~ms}^{-1}$. The drivers of the trains begin to decelerate simultaneously when they are just $2 \mathrm{~km}$ apart. If the decelerations are both uniform and equal, then the value of deceleration to barely avoid collision should be (a) $0.8 \mathrm{~ms}^{-2}$
(b) $2.1 \mathrm{~ms}^{-2}$
(c) $11.0 \mathrm{~ms}^{-2}$ (d) $13.2 \mathrm{~ms}^{-2}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:21

Problem 73

A $210 \mathrm{~m}$ long train is moving due North at a speed of $25 \mathrm{~m} / \mathrm{s}$. A small bird is flying due South, a little above the train with speed $5 \mathrm{~m} / \mathrm{s}$. The time taken by the bird to cross the train is
$\begin{array}{llll}\text { (a) } 6 \mathrm{~s} & \text { (b) } 7 \mathrm{~s} & \text { (c) } 9 \mathrm{~s} & \text { (d) } 10 \mathrm{~s}\end{array}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:59

Problem 74

A police jeep is chasing with velocity of $45 \mathrm{~km} / \mathrm{h}$ a theif in another jeep moving with velocity $153 \mathrm{~km} / \mathrm{h}$. Police fires a bullet with muzzle velocity of $180 \mathrm{~m} / \mathrm{s}$. The velocity with which is will strike of the car of the thief is
$\begin{array}{lll}\text { (a) } 150 \mathrm{~m} / \mathrm{s} & \text { (b) } 27 \mathrm{~m} / \mathrm{s} & \text { (c) } 450 \mathrm{~m} / \mathrm{s}\end{array}$
(d) $250 \mathrm{~m} / \mathrm{s}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:40

Problem 75

A boat is sent across a river with a velocity of $8 \mathrm{~km} / \mathrm{h}$. If the resultant velocity of boat is $10 \mathrm{~km} / \mathrm{h}$, then velocity of river is $\begin{array}{lll}\text { (a) } 10 \mathrm{~km} / \mathrm{h} & \text { (b) } 8 \mathrm{~km} / \mathrm{h} & \text { (c) } 6 \mathrm{~km} / \mathrm{h}\end{array}$
(d) $4 \mathrm{~km} / \mathrm{h}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:41

Problem 76

The distance between two particles moving towards each other is decreasing at the rate of $6 \mathrm{~m} / \mathrm{s}$. If these particles travel with same speed and in the same direction then the separatioon increase at the rate of $4 \mathrm{~m} / \mathrm{s}$. The particles have speed as $\begin{array}{ll}\text { (a) } 5 \mathrm{~m} / \mathrm{s} 1 \mathrm{~m} / \mathrm{s} & \text { (b) } 4 \mathrm{~m} / \mathrm{s} ; 1 \mathrm{~m} / \mathrm{s}\end{array}$
(c) $4 \mathrm{~m} / \mathrm{s} ; 2 \mathrm{~m} / \mathrm{s}$
(d) $5 \mathrm{~m} / \mathrm{s} ; 2 \mathrm{~m} / \mathrm{s}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:45

Problem 77

A train is moving towards east and a car is along north, both with same speed. The observed direction of a car to the passenger in the train is
(a) east-north direction
(b) west-north direction
(c) south-east direction
(d) None of the above

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:52

Problem 78

A boat crosses a river from part $A$ to part $B$ which are just on opposite side. The speed of the water is $v_{w}$ and that of boat is $v_{h}$ relative to still water. Assume $v_{b}=2 v_{w}$. What is the time taken by the boat? If it has to cross the river directly on the $A B$ line.
(a) $\frac{2 D}{v_{b} \sqrt{3}}$
(b) $\frac{\sqrt{3} D}{2 v_{b}}$
(c) $\frac{D}{v_{b} \sqrt{2}}$
(d) $\frac{D \sqrt{2}}{v_{b}}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:53

Problem 79

Two cars $A$ and $B$ are moving with same speed of $45 \mathrm{~km} / \mathrm{h}$ along same direction. If a third car $\mathrm{C}$ coming from the opposite direction with a speed of $36 \mathrm{~km} / \mathrm{h}$ meets two cars in an interval of 5 minutes. The distance between cars $A$ and $B$ should be (in $\mathrm{km}$ )
(a) $6.75$
(b) $7.25$
(c) $5.55$
(d) $8.35$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:43

Problem 80

Two trains $A$ and $B$ of length $400 \mathrm{~m}$ each are moving on two parallel tracks with a uniform speed of $72 \mathrm{~km} / \mathrm{h}$ in the same direction, with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1 \mathrm{~m} / \mathrm{s}^{2}$. If after $50 \mathrm{~s}$, the guard of $B$ just brushes past the driver of $A$, what was the original distance between them?
(a) $1250 \mathrm{~m}$
(b) $1350 \mathrm{~m}$
(c) $1450 \mathrm{~m}$
(d) None of these

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
03:40

Problem 81

On a two lane road, car $A$ is travelling with a speed of $36 \mathrm{~km} / \mathrm{h}$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54 \mathrm{~km} / \mathrm{h}$ each. At a certain instant, when the distance $A B$ is equal to $A C$, both being $1 \mathrm{~km}, B$ decides to overtake $A$ before $C$ does. In this case, the acceleration of car $B$ is required to avoid an accident
(a) $1 \mathrm{~m} / \mathrm{s}^{2}$
(b) $0.1 \mathrm{~m} / \mathrm{s}^{2}$
(c) $1.9 \mathrm{~m} / \mathrm{s}^{2}$
(d) $0.2 \mathrm{~m} / \mathrm{s}^{2}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:28

Problem 82

A passenger arriving in a new town wishes to go from the station to a hotel located $10 \mathrm{~km}$ away on a straight road from the station. A dishonest cabman takes him along a circuitoius path $23 \mathrm{~km}$ long and reaches the hotel in $28 \mathrm{~min}$. What are the average speed of the taxi and the magnitude of average velocity respectively (in $\mathrm{km} / \mathrm{h}) ?$
(a) $49.3$ and $21.43$
(b) $48.3$ and $24.43$
(c) 21 and 20
(d) $21.3$ and $49.3$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:56

Problem 83

A man can swim with a speed of $4 \mathrm{~km} / \mathrm{h}$ in still water. How long does he take to cross a river $1 \mathrm{~km}$ wide, if the river flows steadily $3 \mathrm{~km} / \mathrm{h}$ and he makes his strokes normal to the river current. How far down the river does he go when he reaches the other bank? [NCERT]
(a) $850 \mathrm{~m}$
(b) $750 \mathrm{~m}$
(c) $650 \mathrm{~m}$
(d) None of these

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator