JEE Physics

StemEZ

Chapter 3

Laws Of Motion - all with Video Answers

Educators

Chapter Questions

Problem 327

The velocity of a body of mass $20 \mathrm{~kg}$ decrease from $20 \mathrm{~ms}^{-1}$ to $5 \mathrm{~ms}^{-1}$ in a distance of $100 \mathrm{~m}$. Force on the body is
(A) $-27.5 \mathrm{~N}$
(B) $-47.5 \mathrm{~N}$
(C) $-37.5 \mathrm{~N}$
(D) $-67.5 \mathrm{~N}$

Vysakh M

Vysakh M

Numerade Educator

Problem 328

A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. if the hand moves $0.2 \mathrm{~m}$ while applying the force and the ball goes up to $2 \mathrm{~m}$ height further. find the magnitude of the force. (Consider $\mathrm{g}=10 \mathrm{~ms}^{-1}$ )
(A) $16 \mathrm{~N}$
(B) $20 \mathrm{~N}$
(C) $22 \mathrm{~N}$
(D) $4 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 329

Formula for true force is
(A) $\mathrm{F}=\mathrm{ma}$
(B) $\mathrm{F}=[\{\mathrm{d}(\mathrm{mv})\} / \mathrm{dt}]$
(C) $\mathrm{F}=\mathrm{m}(\mathrm{dv} / \mathrm{dt})$
(D) $F=m\left(d^{2} x / d t^{2}\right)$

Vysakh M

Numerade Educator

Problem 330

A Particle moves in the X-Y plane under the influence of a force such that its linear momentum is $\mathrm{P}^{-}(\mathrm{t})=\mathrm{A}[\mathrm{i} \cos (\mathrm{kt})-\mathrm{j} \sin (\mathrm{kt})]$ where $\mathrm{A}$ and $\mathrm{k}$ are constants.
The angle between the force and momentum is
(A) $0^{\circ}$
(B) $30^{\circ}$
(C) $45^{\circ}$
(D) $90^{\circ}$

Vysakh M

Numerade Educator

Problem 331

Force of $5 \mathrm{~N}$ acts on a body of weight $9.8 \mathrm{~N}$. what is the acceleration produced in $\mathrm{ms}^{-2}$.
(A) $49.00$
(B) $5.00$
(C) $1.46$
(D) $0.51$

Vysakh M

Numerade Educator

Problem 332

A lift is going up. The total mass of the lift and the passenger is $1000 \mathrm{~kg}$ The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $\mathrm{t}=10.5 \mathrm{sec}$ will be
(A) $8000 \mathrm{~N}$
(B) Zero
(C) $12000 \mathrm{~N}$
(D) $17400 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 333

Same force acts on two bodies of different masses $2 \mathrm{~kg}$ and $4 \mathrm{~kg}$ initially at rest. the ratio of times required to acquire same final velocity is
(A) $2: 1$
(B) $1: 2$
(C) $1: 1$
(D) $4: 16$

Vysakh M

Numerade Educator

Problem 334

Which of the following quantities measured from different inertial reference frames are same
(A) Force
(B) Velocity
(C) Displacement
(D) Kinetic Energy

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator

Problem 335

10,000 small balls, each weighing $1 \mathrm{~g}$ strike one square $\mathrm{cm}$ of area per second with a velocity $100 \mathrm{~ms}^{-1}$ in a normal direction and rebound with the same velocity. The value of pressure on the surface will be
(A) $2 \times 10^{3} \mathrm{Nm}^{-2}$
(B) $2 \times 10^{5} \mathrm{Nm}^{-2}$
(C) $10^{7} \mathrm{Nm}^{-2}$
(D) $2 \times 10^{7} \mathrm{Nm}^{2}$

Vysakh M

Numerade Educator

Problem 336

When the speed of a moving body is doubled
(A) Its acceleration is doubled
(B) Its momentum is doubled
(C) Its kinetic energy is doubled
(D) Its potential energy is doubled

Vysakh M

Numerade Educator

Problem 337

A particle moves in the XY Plane under the action of a force $\mathrm{F}$ such that the components of its linear momentum $\mathrm{P}$ at any time $t$ are $P_{x}=2$ cost, $P y=2$ sint. The angle between $F$ and $P$ at time $t$ is
(A) $90^{\circ}$
(B) $0^{\circ}$
(C) $180^{\circ}$
(D) $30^{\circ}$

Vysakh M

Numerade Educator

Problem 338

A player caught a cricket ball of mass $150 \mathrm{~g}$ moving at the rate of $20 \mathrm{~ms}^{-1}$. If the catching process be completed in $0.1 \mathrm{~s}$ the force of the blow exerted by the ball on the hands of player is
(A) $0.3 \mathrm{~N}$
(B) $30 \mathrm{~N}$
(C) $300 \mathrm{~N}$
(D) $3000 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 339

A body of mass $5 \mathrm{~kg}$ starts from the origin with an initial velocity $u^{\rightarrow}=30 \mathrm{i}+40 \mathrm{j} \mathrm{ms}^{-1}$. If a constant Force $\underline{F}=-\left(\mathrm{i}^{\wedge}+5 \mathrm{j}\right) \mathrm{N}$ acts on the body, the time in which the
y-component of the velocity becomes zero is
(A) $5 \mathrm{~s}$
(B) $20 \mathrm{~s}$
(C) $40 \mathrm{~s}$
(D) $80 \mathrm{~s}$

Vysakh M

Numerade Educator

Problem 340

Swimming is possible on account of
(A) First law of motion
(B) second law of motion
(C) Third law of motion
(D) Newton's law of gravitation

Vysakh M

Numerade Educator

Problem 341

A cold soft drink is kept on the balance. When the cap is open, then the weight
(A) Increases
(B) Decreases
(C) First increase then decreases
(D) Remains same

Vysakh M

Numerade Educator

Problem 342

A wagon weighing $1000 \mathrm{~kg}$ is moving with a velocity $50 \mathrm{~km} \mathrm{~h}^{-1}$ on smooth horizontal rails. A mass of $250 \mathrm{~kg}$ is dropped into it. The velocity with which it moves now is
(A) $2.5 \mathrm{~km} \mathrm{~h}^{-1}$
(B) $20 \mathrm{~km} \mathrm{~h}^{-1}$
(C) $40 \mathrm{~km} \mathrm{~h}^{-1}$
(D) $50 \mathrm{~km} \mathrm{~h}^{-1}$

Vysakh M

Numerade Educator

Problem 343

The Figure shows the Position-time $(\mathrm{x}-\mathrm{t})$ graph of one dimensional motion of a body of mass The magnitude of each impulse is
(A) $0.2 \mathrm{Ns}$
(B) $0.4 \mathrm{Ns}$
(C) $0.8 \mathrm{Ns}$
(D) $1.6 \mathrm{Ns}$

Vysakh M

Numerade Educator

Problem 344

Three Forces $F_{1}, F_{2}$, and $F_{3}$ together keep a body in equilibrium. If $F_{1}=3 \mathrm{~N}$ along the positive $\mathrm{X}$ - axis, $\mathrm{F}_{2}=4 \mathrm{~N}$ along the positive Y-axis then the third force $F_{3}$ is
(A) $5 \mathrm{~N}$ -making an angle $\theta=\tan ^{-1}(3 / 4)$ with negative $\mathrm{y}$ -axis
(B) $5 \mathrm{~N}$ -making an angle $\theta=\tan ^{-1}(4 / 3)$ with negative $\mathrm{y}$ -axis
(C) $7 \mathrm{~N}$ -making an angle $\theta=\tan ^{-1}(3 / 4)$ with negative $\mathrm{y}$ -axis
(D) $7 \mathrm{~N}$ -making an angle $\theta=\tan ^{-1}(4 / 3)$ with negative $\mathrm{y}$ -axis

Narayan Hari

Numerade Educator

Problem 345

A solid sphere of mass $2 \mathrm{~kg}$ is resting inside a cube as shown in the figure. The cube is moving with a velocity $\mathrm{v} \rightarrow=(5 \mathrm{t} \mathrm{i}+2 \mathrm{t} \mathrm{j}) \mathrm{ms}^{-1}$ Here $\mathrm{t}$ is the time in second. All
surfaces are smooth. The sphere is at rest with respect to the cube. what is the total force exerted by the sphere on the cube $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $\sqrt{29 \mathrm{~N}}$
(B) $29 \mathrm{~N}$
(C) $26 \mathrm{~N}$
(D) $\sqrt{89 \mathrm{~N}}$

Vysakh M

Numerade Educator

Problem 346

A particle of mass $2 \mathrm{~kg}$ is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is
(A) $10 \mathrm{~ms}^{-1}$
(B) $20 \mathrm{~ms}^{-1}$
(C) $75 \mathrm{~ms}^{-1}$
(D) $50 \mathrm{~ms}^{-1}$

Vysakh M

Numerade Educator

Problem 347

A block of mass $4 \mathrm{~kg}$ is placed on a rough horizontal plane. A time dependent force $\mathrm{F}=\mathrm{Kt}^{2}$ acts on a block, where $\mathrm{k}=2 \mathrm{~N} / \mathrm{s}^{2}$, co-efficient of friction $\mu=0.8$. Force of friction between the block and the plane at $\mathrm{t}=2 \mathrm{~S}$ is....
(A) $32 \mathrm{~N}$
(B) $4 \mathrm{~N}$
(C) $2 \mathrm{~N}$
(D) $8 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 348

A $7 \mathrm{~kg}$ object is subjected to two forces (in newton) $\underline{F}_{1}=20 \mathrm{i}^{-}+30 \mathrm{j}^{-}$ and $\underline{\mathrm{F}}_{2}=8 \mathrm{i}^{-}-5 \mathrm{j}$ `The magnitude of
resulting acceleration in $\mathrm{ms}^{-2}$ will be
(A) 5
(B) 4
(C) 3
(D) 2

Vysakh M

Numerade Educator

Problem 349

A car travelling at a speed of $30 \mathrm{~km} / \mathrm{h}$ is brought to a halt in 8 meters by applying brakes. If the same car is travelling at $60 \mathrm{~km} / \mathrm{h}$ it can be brought to a halt with the same breaking power in
(A) $8 \mathrm{~m}$
(B) $16 \mathrm{~m}$
(C) $24 \mathrm{~m}$
(D) $32 \mathrm{~m}$

Vysakh M

Numerade Educator

Problem 350

A given object takes n times more time to slide down $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is
(A) $\left[1 /\left(2-\mathrm{n}^{2}\right)\right]$
(B) $\left[1-\left(1 / \mathrm{n}^{2}\right)\right]$

Vysakh M

Numerade Educator

Problem 351

Two bodies of equal masses revolve in circular orbits of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ with the same period Their centripetal forces are in the ratio.
(A) $\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)^{2}$
(B) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)$
(C) $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}$
(D) $\left.\sqrt{(}_{1} R_{2}\right)$

Vysakh M

Numerade Educator

Problem 352

Two masses $\mathrm{M}$ and $(\mathrm{M} / 2)$ are joined together by means of light inextensible string passed over a frictionless pulley as shown in fig. When the bigger mass is released, the small one will ascend with an acceleration
(A) $(\mathrm{g} / 3)$
(B) $(3 \mathrm{~g} / 2)$
(C) $\mathrm{g}$
(D) $(\mathrm{g} / 2)$

Vysakh M

Numerade Educator

Problem 353

A $0.5 \mathrm{~kg}$ ball moving with a speed of $12 \mathrm{~ms}^{-1}$ strikes a hard wall at an angle of $30^{\circ}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for $0.25 \mathrm{~S}$ the average force acting on the wall is
(A) $96 \mathrm{~N}$
(B) $48 \mathrm{~N}$
(C) $24 \mathrm{~N}$
(D) $12 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 354

A shell of mass $200 \mathrm{~g}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that generates $1.05 \mathrm{KJ}$ of energy. The initial velocity of the shell is
(A) $100 \mathrm{~m} / \mathrm{s}$
(B) $80 \mathrm{~ms}^{-1}$
(C) $40 \mathrm{~ms}^{-1}$
(D) $120 \mathrm{~ms}^{-1}$

Vysakh M

Numerade Educator

Problem 355

A gramophone record is revolving with an angular velocity
$w$. A coin is placed at a distance $r$ from the centre of the record. The coefficient of static friction is. The coin will revolve with the record if
(A) $\mathrm{r}=\mathrm{gw}^{2}$
(B) $\mathrm{r}<\left(\mathrm{w}^{2} / \mathrm{g}\right)$
(C) $r<\left(g / w^{2}\right)$
(D) $r \geq\left(g / w^{2}\right)$

Narayan Hari

Numerade Educator

Problem 356

A stone of mass $2 \mathrm{~kg}$ is tied to a string of length $0.5 \mathrm{~m}$ It the breaking tension of the string is $900 \mathrm{~N}$, then the maximum angular velocity the stone can have in uniform circular motion is
(A) $30 \mathrm{rad} / \mathrm{s}$
(B) $20 \mathrm{rad} / \mathrm{s}$
(C) $10 \mathrm{rad} / \mathrm{s}$
(D) $25 \mathrm{rad} / \mathrm{s}$

Vysakh M

Numerade Educator

Problem 357

A body of mass $6 \mathrm{~kg}$ is hanging from another body of mass $10 \mathrm{~kg}$ as shown in fig. This combination is being pulled up by a string with an acceleration of $2 \mathrm{~ms}^{-2}$. the tension $\mathrm{T}_{1}$ is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $240 \mathrm{~N}$
(B) $150 \mathrm{~N}$
(C) $220 \mathrm{~N}$
(D) $192 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 358

A sparrow flying in air sits on a stretched telegraph wire. If the weight of the sparrow is $\mathrm{W}$, which of the following is true about the tension T produced in the wire?
(A) $\mathrm{T}=\mathrm{W}$
(B) $\mathrm{T}<\mathrm{W}$
(C) $\mathrm{T}=0$
(D) $\mathrm{T}>\mathrm{W}$

Vysakh M

Numerade Educator

Problem 359

Fig. shows the displacement of a particle going along $\mathrm{X}$ -axis as a function of time. The force acting on the particle is zero in the region
(A) $\mathrm{AB}$
(B) $\mathrm{BC}$
(C) $\mathrm{CD}$
(D) None of these

Narayan Hari

Numerade Educator

Problem 360

A Force $(F)$ varies with time $(t)$ as shown in fig. Average force over a complete cycle is-
(A) Zero
(B) $\left(\mathrm{F}_{0} / \sqrt{2}\right)$
(C) $\left(\mathrm{F}_{0} / \pi\right)$
(D) $2 \mathrm{~F}_{0}$

Vysakh M

Numerade Educator

Problem 361

A body of mass $0.05 \mathrm{~kg}$ is falling with acceleration $9.4 \mathrm{~ms}^{-2}$. The force exerted by air opposite to motion is $\mathrm{N}$
$\left(g=9.8 \mathrm{~ms}^{-2}\right)$
(A) $0.02$
(B) $0.20$
(C) $0.030$
(D) Zero

Vysakh M

Numerade Educator

Problem 362

The average force necessary to stop a hammer with 25 NS momentum in $0.04 \mathrm{sec}$ is $\quad \mathrm{N}$
(A) 625
(B) 125
(C) 50
(D) 25

Vysakh M

Numerade Educator

Problem 363

Newton's third law of motion leads to the law of conservation of
(A) Angular momentum
(B) Energy
(C) mass
(D) momentum

Narayan Hari

Numerade Educator

Problem 364

A ball falls on surface from $10 \mathrm{~m}$ height and rebounds to $2.5 \mathrm{~m} .$ If duration of contact with floor is $0.01 \mathrm{sec}$. then average acceleration during contact is $\mathrm{ms}^{-2}$
(A) 2100
(B) 1400
$\begin{array}{ll}\text { (C) } 700 & \text { (D) } 400\end{array}$

Vysakh M

Numerade Educator

Problem 365

A vehicle of $100 \mathrm{~kg}$ is moving with a velocity of $5(\mathrm{~m} / \mathrm{s})$. To stop it in $(1 / 10) \mathrm{sec}$, the required force in opposite direction is $\mathrm{N}$
(A) 50
(B) 500
(C) 5000
(D) 1000

Vysakh M

Numerade Educator

Problem 366

The linear momentum $\mathrm{P}$ of a particle varies with the time as follows. $P=a+b t^{2}$ Where $a$ and $b$ are constants. The net force acting on the particle is
(A) Proportional to t
(B) Proportional to t $^{2}$
(C) Zero
(D) constant

Vysakh M

Numerade Educator

Problem 367

A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. which of the following diagram represents the surface of the liquid?

Vysakh M

Numerade Educator

Problem 368

A body of $2 \mathrm{~kg}$ has an initial speed $5 \mathrm{~m} / \mathrm{s}$. A force act on it for some time in the direction of motion. The force
(F) time (t) graph is shown in figure. The final speed of the body is
(A) $9.25 \mathrm{~ms}^{-1}$
(B) $5 \mathrm{~ms}^{-1}$
(C) $14.25 \mathrm{~ms}^{-1}$
(D) $4.25 \mathrm{~ms}^{-1}$

Vysakh M

Numerade Educator

Problem 369

which of the following statement is correct?
(A) A body has a constant velocity but a varying speed.
(B) A body has a constant speed but a varying value of acceleration.
(C) A body has a constant speed and zero acceleration.
(D) A body has a constant speed but velocity is zero.

Vysakh M

Numerade Educator

Problem 370

A force of $8 \mathrm{~N}$ acts on an object of mass $5 \mathrm{~kg}$ in $\mathrm{X}$ -direction and another force of $6 \mathrm{~N}$ acts on it in $\mathrm{Y}$ -direction. Hence, the magnitude of acceleration of object will be
(A) $1.5 \mathrm{~ms}^{-2}$
(B) $2.0 \mathrm{~ms}^{-2}$ (C) $2.5 \mathrm{~ms}^{-2}$
(D) $3.5 \mathrm{~ms}^{-2}$

Vysakh M

Numerade Educator

Problem 371

Three forces are acting simultaneously on a particle moving with velocity $\mathrm{V}^{-}$. These forces are represented in magnitude and direction by the three sides of a triangle $\mathrm{ABC}$. The particle will now move with velocity (A) Less than $\mathrm{v}^{\rightarrow}$
(B) greater than $\mathrm{v}^{\rightarrow}$
(C) $\left|\mathrm{v}^{-}\right|$ in the direction of the largest force $\mathrm{BC}$
(D) $\mathrm{v}^{\rightarrow}$ remaining unchanged.

Vysakh M

Numerade Educator

Problem 372

A plate of mass $\mathrm{M}$ is placed on a horizontal frictionless surface and a body of mass $m$ is placed on this plate, The coefficient of dynamic friction between this body and the plate is $\mu$. If a force $2 \mu \mathrm{mg}$. is applied to the body of mass $\mathrm{m}$ along the horizontal direction the acceleration of the plate will be
(A) $(\mu \mathrm{m} / \mathrm{M}) \mathrm{g}$
(B) $[\mu \mathrm{m} /(\mathrm{M}+\mathrm{m})] \mathrm{g}$
(C) $[(2 \mu \mathrm{m}) / \mathrm{M}] \mathrm{g}$
(D) $[(2 \mu \mathrm{m}) /(\mathrm{M}+\mathrm{m})] \mathrm{g}$

Narayan Hari

Numerade Educator

Problem 373

On the horizontal surface of a truck $(=0.6)$, a block of mass $1 \mathrm{~kg}$ is placed. If the truck is accelerating at the rate of $5 \mathrm{~m} / \mathrm{s}^{2}$ then frictional force on the block will be $\mathrm{N}$
(A) 5
(B) 6
(C) $5.88$
(D) 8

Vysakh M

Numerade Educator

Problem 374

Two blocks of mass $8 \mathrm{~kg}$ and $4 \mathrm{~kg}$ are connected a heavy string Placed on rough horizontal Plane, The $4 \mathrm{~kg}$ block is Pulled with a constant force $\mathrm{F}$. The co-efficient of friction between the blocks and the ground is $0.5$, what is the value of $F$, So that the tension in the spring is constant throughout during the motion of the blocks? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $40 \mathrm{~N}$
(B) $60 \mathrm{~N}$
(C) $50 \mathrm{~N}$
(D) $30 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 375

Seven blocks, each of mass $1 \mathrm{~kg}$ are arranged one above the other as shown in figure. what are the values of the contact forces exerted on the third block by the forth and the second block respectively ? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $40 \mathrm{~N}, 50 \mathrm{~N}$
(B) $50 \mathrm{~N}, 40 \mathrm{~N}$
(C) $40 \mathrm{~N}, 20 \mathrm{~N}$
(D) $50 \mathrm{~N}, 30 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 376

A man is standing on a spring balance. Reading of spring balance is $60 \mathrm{~kg} \mathrm{f}$. If man jumps outside balance, then reading of spring balance
(A) First increase than decreases to zero
(B) Decreases
(C) Increases
(D) Remains same

Vysakh M

Numerade Educator

Problem 377

A car turns a corner on a slippery road at a constant speed of $10 \mathrm{~m} / \mathrm{s}$. If the coefficient of friction is $0.5$, the minimum radius of the arc at which the car turns is meter.
(A) 20
(B) 10
(C) 5
(D) 4

Vysakh M

Numerade Educator

Problem 378

A person standing on the floor of a lift drops a coin. The coin reaches the floor of the lift in time if the lift is stationary and the time $\mathrm{t}_{2}$ if it is accelerated in upward direction. Than
(A) $t_{1}=t_{2}$
(B) $\mathrm{t}_{1}>\mathrm{t}_{2}$
(C) $t_{1}<t_{2}$
(D) Cannot say anything

Narayan Hari

Numerade Educator

Problem 379

A lift of mass $1000 \mathrm{~kg}$ is moving with an acceleration of $1 \mathrm{~ms}^{-2}$ in upward direction Tension developed in the rope of lift is $\mathrm{N}\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$
(A) 9800
(B) 10,000
(C) 10,800
(D) 11,000

Vysakh M

Numerade Educator

Problem 380

Three blocks of masses $m_{1}, m_{2}$ and $m_{3}$ are connected by mass less strings as shown in figure, on a frictionless table. They are Pulled with a force $\mathrm{T}_{3}=40 \mathrm{~N}$. If $\mathrm{m}_{1}=10 \mathrm{~kg}$, $\mathrm{m}_{2}=6 \mathrm{~kg}$ and $\mathrm{m}_{3}=4 \mathrm{~kg}$ the tension $\mathrm{T}_{2}$ will be $=$
$\mathrm{N}$
(A) 20
(B) 40
(C) 10
(D) 32

Vysakh M

Numerade Educator

Problem 381

If the surfaces shown in figure are frictionless, the ratio of $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ is
(A) $\sqrt{3}: 2$
(B) $1: \sqrt{3}$
(C) $1: 5$
(D) $5: 1$

Vysakh M

Numerade Educator

Problem 382

Three masses $1 \mathrm{~kg}, 6 \mathrm{~kg}$ and $3 \mathrm{~kg}$ are connected to each other with threads and are placed on a table as shown in figure. The acceleration with which the system is moving
is $\mathrm{ms}^{-2}\left(\mathrm{~g}=10 \mathrm{~ms}^{-2}\right)$
$\begin{array}{lll}\text { (A) zero } & \text { (B) } 1 & \text { (C) } 2\end{array}$
(D) 3

Narayan Hari

Numerade Educator

Problem 383

A rope which can withstand a maximum tension of $400 \mathrm{~N}$ hangs from a tree. If a monkey of mass $30 \mathrm{~kg}$ climbs on the rope in which of the following cases-will the rope break? (take $g=10 \mathrm{~ms}^{-}{ }^{2}$ and neglect the mass of rope $)$
(A) When the monkey climbs with constant speed of $5 \mathrm{~ms}^{-1}$
(B) When the monkey climbs with constant acceleration of $2 \mathrm{~ms}^{-2}$
(C) When the monkey climbs with constant acceleration of $5 \mathrm{~ms}^{-2}$
(D) When the monkey climbs with the constant speed of $12 \mathrm{~ms}^{-1}$

Narayan Hari

Numerade Educator

Problem 384

An object of mass $3 \mathrm{~kg}$ is moving with a velocity of $5 \mathrm{~m} / \mathrm{s}$ along a straight path. If a force of $12 \mathrm{~N}$ is applied for $3 \mathrm{sec}$ on the object in a perpendicular to its direction of motion. The magnitude of velocity of the particle at the end of $3 \mathrm{sec}$ is $\mathrm{m} / \mathrm{s}$.
(A)
(B) 12
(C) 13
(D) 4

Narayan Hari

Numerade Educator

Problem 385

Same forces act on two bodies of different mass $2 \mathrm{~kg}$ and $5 \mathrm{~kg}$ initially at rest. The ratio of times required to acquire same final velocity is
(A) $5: 3$
(B) $25: 4$
(C) $4: 25$
(D) $2: 5$

Vysakh M

Numerade Educator

Problem 386

A body of mass $5 \mathrm{~kg}$ starts motion form the origin with an initial velocity $\mathrm{v}_{0} \rightarrow=30 \mathrm{i}+40 \mathrm{j} \mathrm{m} / \mathrm{s}$ If a constant force
$\mathrm{F}=-\left(\mathrm{i}^{\wedge}+5 \mathrm{j}\right) \mathrm{N}$ acts on the body, than the time in which the Y-component of the velocity becomes zero is
(A) $5 \mathrm{~s}$
(B) $20 \mathrm{~s}$
(C) $40 \mathrm{~s}$
(D) $80 \mathrm{~s}$

Vysakh M

Numerade Educator

Problem 387

A Block of mass $300 \mathrm{~kg}$ is set into motion on a frictionless horizontal surface with the help of frictionless pulley and a rope system as shown in figure. What horizontal force $\mathrm{F}$ should be applied to produce in the block an acceleration of $1 \mathrm{~ms}^{-2} ?$
(A) $150 \mathrm{~N}$
(B) $100 \mathrm{~N}$
(C) 300
(D) $50 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 388

A body of mass $\mathrm{m}$ rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the body is Pulled by a force $P$ as shown in figure, the limiting friction between body and surface will be
(A) $\mu \mathrm{mg}$
(B) $\mu[\mathrm{mg}+(\mathrm{P} / 2)]$
(C) $\mu[\mathrm{mg}-(\mathrm{P} / 2)]$
(D) $\mu[\mathrm{mg}-(\sqrt{3} \mathrm{P} / 2)]$

Vysakh M

Numerade Educator

Problem 389

Three blocks $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ of equal mass $\mathrm{m}$ are placed one over the other, one on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ is $0.5$. What would be the maximum value of mass of block $D$ so that the blocks $A, B$ and $C$ move without slipping over each other?
(A) $3 \mathrm{~m}$
(B) $5 \mathrm{~m}$
(C) $6 \mathrm{~m}$
(D) $4 \mathrm{~m}$

Narayan Hari

Numerade Educator

Problem 390

A train moving along a horizontal track. A pendulum suspended from the roof makes an angle of $4^{\circ}$ with the vertical, The acceleration of the train is $\mathrm{ms}^{-2}\left(\mathrm{~g}=10 \mathrm{~ms}^{-2}\right)$
(A) $0.6$
(B) $0.7$
(C) $0.5$
(D) $0.2$

Vysakh M

Numerade Educator

Problem 391

A bag of sand of mass $\mathrm{m}$ is suspended by rope. a bullet of mass $(\mathrm{m} / 30)$ is fired at it with a velocity $\mathrm{V}$ and gets embedded into it. The velocity of the bag finally is
(A) $(31 \mathrm{~V} / 30)$
(B) $(30 \mathrm{~V} / 31)$
(C) $(\mathrm{V} / 31)$
(D) $(\mathrm{V} / 30)$

Narayan Hari

Numerade Educator

Problem 392

Three blocks having equal mass of $2 \mathrm{~kg}$ are hanging on a string passing over a pulley as shown in figure. what will be the tension produced in a string connecting the blocks $B$ and $\mathrm{C}$ (A) zero
(B) $13.1 \mathrm{~N}$
(C) $3.3 \mathrm{~N}$
(D) $19.6 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 393

A partly hanging uniform chain of length $\mathrm{L}$ is resting on a rough horizontal table. $\ell$ is the maximum possible length that can hang in equilibrium The coefficient of friction between the chain and table is
(A) $[\ell \mathrm{L} /(\mathrm{L}+\ell)]$
(B) $(\mathrm{L} / \ell)$
(C) $(\ell / \mathrm{L})$
(D) $[\ell /(\mathrm{L}-\ell)]$

Narayan Hari

Numerade Educator

Problem 394

As shown in figure, the block of $2 \mathrm{~kg}$ at one end and the other of $3 \mathrm{~kg}$ at the other end of a light string are connected. It the system remains stationary find the magnitude and direction of the frictional force $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $20 \mathrm{~N}$, downward on slope
(B) $20 \mathrm{~N}$, upward on slope
(C) $10 \mathrm{~N}$, downward on slope
(D) $10 \mathrm{~N}$ upward on slope

Vysakh M

Numerade Educator

Problem 395

A particle is resting over a smooth horizontal floor, At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $\mathrm{F}=\alpha \mathrm{t}$, where $\alpha=$ is constant Match the column after seeing the figure.
Column-1 $\quad$ Column-2
(a) curve
(i) shows.
(p) velocity against time
(b) curve
(ii) shows
(q) velocity against acceleration
(r) acceleration against time
(A) (i) - p (ii)-q
(B) (i) - q (ii) - r
(C) (i) - r (ii) - p
$(\mathrm{D})(\mathrm{i})-\mathrm{q}(\mathrm{ii})-\mathrm{p}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 396

A car of mass $1000 \mathrm{~kg}$ travelling at $32 \mathrm{~m} / \mathrm{s}$ clashes into a rear of a truck of mass $8000 \mathrm{~kg}$ moving in the same direction with a velocity of $4 \mathrm{~m} / \mathrm{s}$. After the collision the car bounces with a velocity of $8 \mathrm{~ms}^{-1}$. The velocity of truck after the impact is $\mathrm{m} / \mathrm{s}$
(B) 4
(C) 6
(D) 9
(A) 8

Vysakh M

Numerade Educator

Problem 397

A Block of mass $\mathrm{m}=2 \mathrm{~kg}$ is resting on a rough inclined plane of inclination 300 as shown in figure. The coefficient of friction between the block and the plane is $\mu=0.5$. What minimum force $\mathrm{F}$ should be applied perpendicular to the plane of block so that block does not slip on the plane ? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) zero
(B) $6.24 \mathrm{~N}$
(C) $2.68 \mathrm{~N}$
(D) $4.3 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 398

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough A body starting from the rest at top come back to rest at the bottom, then the coefficient of friction for the lower half is given by
(A) $\mu=\sin \theta$
(B) $\mu=\cot \theta$
(C) $\mu=2 \cos \theta$
(D) $\mu=2 \tan \theta$

Narayan Hari

Numerade Educator

Problem 399

A Block of mass $\mathrm{m}=4 \mathrm{~kg}$ is placed over a rough inclined plane as shown in figure, The coefficient of friction between the block and plane is $\mu=0.6 .$ A force $F=10 \mathrm{~N}$ is applied on the block of an angle at $30^{\circ}$. The contact force between the block and the plane is
(A) $27.15 \mathrm{~N}$
(B) $16.32 \mathrm{~N}$
(C) $10.65 \mathrm{~N}$
(D) $32.16 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 400

The motion of a particle of a mass $m$ is describe by $\mathrm{y}=\mathrm{ut}+(1 / 2) \mathrm{gt}^{2}$. Find the force acting on the particle.
(A) $\mathrm{F}=\mathrm{ma}$
(B) $\mathrm{F}=\mathrm{mg} \quad$ (C) $\mathrm{F}=0$
(D) None of these

Vysakh M

Numerade Educator

Problem 401

A balloon has a mass of $10 \mathrm{~g}$ in air, The air escapes from the balloon at a uniform rate with a velocity of $5 \mathrm{~cm} / \mathrm{s}$ and the balloon shrinks completely in $2.5 \mathrm{sec}$. calculate the average force acting on the balloon.
(A) 20 dyne
(B) 5 dyne
(C) 0 dyne
(D) 10 dyne

Vysakh M

Numerade Educator

Problem 402

Two bodies $\mathrm{A}$ and $\mathrm{B}$ each of mass $\mathrm{m}$ are fixed together by a mass less spring A force $\mathrm{F}$ acts on the mass $\mathrm{B}$ as shown in figure. At the instant shown, a body $\mathrm{A}$ has an acceleration a. what is the acceleration of $\mathrm{B}$ ?
(A) $[(\mathrm{F} / \mathrm{m})-\mathrm{a}]$
(B) $\mathrm{F}-\mathrm{T}$
(C) $[\mathrm{a}-(\mathrm{F} / \mathrm{m})]$
(D) a

Vysakh M

Numerade Educator

Problem 403

With what acceleration (a) should a box descend so that a block of mass $\mathrm{M}$ placed in it exerts a force $(\mathrm{Mg} / 4)$ on the floor of the box?
(A) $(4 \mathrm{~g} / 3)$
(B) $(3 \mathrm{~g} / 4)$
(C) $\mathrm{g} / 4$
(D) $3 \mathrm{~g}$

Narayan Hari

Numerade Educator

Problem 404

A mass of $6 \mathrm{~kg}$ is suspended by a rope of length $2 \mathrm{~m}$ form the ceiling. A force of $50 \mathrm{~N}$ in the horizontal direction is applied at the mid Point $\mathrm{P}$ of the rope-as shown in figure. what is the angle the rope makes with the vertical in equilibrium ? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$ Neglect mass of the rope.
(A) $40^{\circ}$
(B) $30^{\circ}$
(C) $35^{\circ}$
(D) $45^{\circ}$

Narayan Hari

Numerade Educator

Problem 405

The minimum force required to start pushing a body up a rough (coefficient of) inclined plane is $\mathrm{F}_{1}$. While the minimum force needed to prevent it from sliding down is $\mathrm{F}_{2}$. If the inclined plane makes an angle $\theta$ from the horizontal. such that $\tan \theta=2 \mu$ than the ratio $\left(\mathrm{F}_{1} / \mathrm{F}_{2}\right)$ is
(A) 4
(B) 1
(C) 2
(D) 3

Narayan Hari

Numerade Educator

Problem 406

When forces $\mathrm{F}_{1}, \mathrm{~F}_{2}, \mathrm{~F}_{3}$ are acting on a particle of mass $\mathrm{m}$ such that $\mathrm{F}_{2}$ and $\mathrm{F}_{3}$ are mutually perpendicular, then the particle remains stationary. If the force $F_{1}$ is now removed than the acceleration of the particle is
(A) $\left(\underline{F}_{1} / \mathrm{m}\right)$
(B) $\left(\mathrm{F}_{1} \mathrm{~F}_{2} / \mathrm{m}\right)$
(C) $\left[\left(\mathrm{F}_{2}-\mathrm{F}_{3}\right) / \mathrm{m}\right]$
(D) $\left(\mathrm{F}_{2} / \mathrm{m}\right)$

Narayan Hari

Numerade Educator

Problem 407

Assertion and reason are given in following question. Each question have four options. One of them is correct select it.
(A) Assertion is true. Reason is true and reason is correct explanation for Assertion.
(B) Assertion is true. Reason is true but reason is not the correct explanation of assertion.
(C) Assertion is true. Reason is false.
(D) Assertion is false. Reason is true. Assertion: Frictional forces are conservative forces. Reason: Potential energy can be associated with frictional forces.
(A) a
(B) $b$
(C) $c$
(D) $\mathrm{d}$

Vysakh M

Numerade Educator

Problem 408

Assertion and reason are given in following question. Each question have four options. One of them is correct select it.
(A) Assertion is true. Reason is true and reason is correct explanation for Assertion.
(B) Assertion is true. Reason is true but reason is not the correct explanation of assertion.
(C) Assertion is true. Reason is false.
(D) Assertion is false. Reason is true. Assertion: A body of mass $1 \mathrm{~kg}$ is moving with an acceleration of $1 \mathrm{~ms}^{-1}$ The rate of change of its momentum is $1 \mathrm{~N}$. Reason: The rate of change of momentum of body $=$ force applied on the body.
(A) a
(B) $\mathrm{b}$
(C)
(D) $\mathrm{d}$

Vysakh M

Numerade Educator

Problem 409

Assertion and reason are given in following question. Each question have four options. One of them is correct select it.
(A) Assertion is true. Reason is true and reason is correct explanation for Assertion.
(B) Assertion is true. Reason is true but reason is not the correct explanation of assertion.
(C) Assertion is true. Reason is false.
(D) Assertion is false. Reason is true. Assertion: A body falling freely under gravity becomes weightless. Reason : $R=m(g-a)=m(g-g)=0$
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$

Vysakh M

Numerade Educator

Problem 410

Assertion and reason are given in following question. Each question have four options. One of them is correct select it.
(A) Assertion is true. Reason is true and reason is correct explanation for Assertion.
(B) Assertion is true. Reason is true but reason is not the correct explanation of assertion.
(C) Assertion is true. Reason is false.
(D) Assertion is false. Reason is true. Assertion: It is difficult to move bike with its breaks on. Reason: Rolling friction is converted into sliding friction, which is comparatively larger.
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

Vysakh M

Numerade Educator

Problem 411

A cricket ball of mass $150 \mathrm{~g}$. is moving with a velocity of $12 \mathrm{~m} / \mathrm{s}$ and is hit by a bat so that the ball is turned back with a velocity of $20 \mathrm{~m} / \mathrm{s}$. If duration of contact between the ball and the bat is $0.01 \mathrm{sec}$. The impulse of the force is
(A) $7.4 \mathrm{NS}$
(B) $4.8 \mathrm{NS}$
(C) $1.2 \mathrm{NS}$
(D) $4.7 \mathrm{NS}$

Vysakh M

Numerade Educator

Problem 412

Average force exerted by the bat is
(A) $480 \mathrm{~N}$
(B) $120 \mathrm{~N}$
(C) $1200 \mathrm{~N}$
(D) $840 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 413

The force acting on a body whose linear momentum changes by $20 \mathrm{kgms}^{-1}$ in $10 \mathrm{sec}$ is
(A) $2 \mathrm{~N}$
(B) $20 \mathrm{~N}$
(C) $200 \mathrm{~N}$
(D) $0.2 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 414

An impulsive force of $100 \mathrm{~N}$ acts on a body for $1 \mathrm{sec}$ What is the change in its linear momentum ?
(A) $10 \mathrm{~N}-\mathrm{S}$
(B) $100 \mathrm{~N}-\mathrm{S}$
(C) $1000 \mathrm{~N}-\mathrm{S}$
(D) $1 \mathrm{~N}-\mathrm{S}$

Vysakh M

Numerade Educator

Problem 415

Match the column
\begin{tabular}{l|l} Column - I & Column - II \end{tabular}
(a) Body line on a
(p) is a self adjusting horizontal surface $\quad$ force
(b) Static friction
(q) is a maximum value of static friction
(c) Limiting friction
(r) is then limiting friction
(d) Dynamic friction
(s) force of friction $=0$
(A) $\mathrm{a}-\mathrm{s}, \mathrm{b}-\mathrm{p}, \mathrm{c}-\mathrm{q}, \mathrm{d}-\mathrm{r}$
(B) $\mathrm{a}-\mathrm{p}, \mathrm{b}-\mathrm{q}, \mathrm{c}-\mathrm{r}, \mathrm{d}-\mathrm{s}$
(C) $\mathrm{a}-\mathrm{s}, \mathrm{b}-\mathrm{r}, \mathrm{c}-\mathrm{q}, \mathrm{d}-\mathrm{p}$
(D) $\mathrm{a}-\mathrm{r}, \mathrm{b}-\mathrm{q}, \mathrm{c}-\mathrm{p}, \mathrm{d}-\mathrm{s}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 416

A block B, placed on a horizontal surface is pulled with initial velocity $\mathrm{V}$. If the coefficient of kinetic friction between surface and block is $\mu$, than after how much time, block will come to rest?
(A) (v/g)
(B) $(\mathrm{g} / \mathrm{v})$
(C) $(\mathrm{g} / \mathrm{v})$
(D) $(\mathrm{v} / \mathrm{g})$

Narayan Hari

Numerade Educator

Problem 417

As shown in figure a block of mass $\mathrm{m}$ is attached with a cart. If the coefficient of static friction between the surface of cart and block is $\mu$ than what would be acceleration $\alpha$ of cart to prevent the falling of block?
(A) $\alpha>(\mathrm{mg} / \mu)$
(B) $\alpha>(\mathrm{g} / \mathrm{m})$
(C) $\alpha \geq(\mathrm{g} / \mu)$
(D) $\alpha<(g / \mu)$

Narayan Hari

Numerade Educator

Problem 418

A particle of mass $\mathrm{m}$ is at rest at $\mathrm{t}=0 .$ The force exerting on it in $\mathrm{x}$ -direction is $\mathrm{F}(\mathrm{t})=\mathrm{F} \mathrm{e}^{-\mathrm{bt}}$. Which one of the following graph is of speed $\mathrm{V}(\mathrm{t}) \rightarrow \mathrm{t}$

Narayan Hari

Numerade Educator