JEE Physics

StemEZ

Chapter 4

Work Energy and Power - all with Video Answers

Educators

Chapter Questions

Problem 419

How much is the work done in pulling up a block of wood weighing $2 \mathrm{KN}$ for a length of $10 \mathrm{~m}$ on a smooth plane inclined at an angle of $30^{\circ}$ with the horizontal?
(A) $1.732 \mathrm{KJ}$
(B) $17.32 \mathrm{KJ}$
(C) $10 \mathrm{KJ}$
(D) $100 \mathrm{KJ}$

Narendra Kumar

Narendra Kumar

Numerade Educator

Problem 420

A force of $7 \mathrm{~N}$, making an angle $\theta$ with the horizontal, acting on an object displaces it by $0.5 \mathrm{~m}$ along the horizontal direction. If the object gains K.E. of $2 \mathrm{~J}$, what is the horizontal component of the force?
(A) $2 \mathrm{~N}$
(B) $4 \mathrm{~N}$
(C) $1 \mathrm{~N}$
(D) $14 \mathrm{~N}$

Narendra Kumar

Numerade Educator

Problem 421

A $60 \mathrm{~kg}$ JATAN with $10 \mathrm{~kg}$ load on his head climbs 25 steps of $0.20 \mathrm{~m}$ height each. What is the work done in climbing ? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $5 \mathrm{~J}$
(B) $350 \mathrm{~J}$
(C) $100 \mathrm{~J}$
(D) $3500 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 422

A ball of mass $5 \mathrm{~kg}$ is striding on a plane with initial velocity of $10 \mathrm{~m} / \mathrm{s}$. If co-efficient of friction between surface and ball is $(1 / 2)$, then before stopping it will describe $\ldots \ldots$ $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $12.5 \mathrm{~m}$
(B) $5 \mathrm{~m}$
(C) $7.5 \mathrm{~m}$
(D) $10 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 423

The relationship between force and position is shown in the figure given (in one dimensional case) calculate the work done by the force in displacing a body from $x=0 \mathrm{~cm}$ to $\mathrm{x}=5 \mathrm{~cm}$
(A) 30 ergs
(B) 70 ergs
(C) 20 ergs
(D) 60 ergs

Narendra Kumar

Numerade Educator

Problem 424

The force constant of a wire is $\mathrm{K}$ and that of the another wire is $3 \mathrm{k}$ when both the wires are stretched through same distance, if work done are $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$, then...
(A) $\mathrm{w}_{2}=3 \mathrm{w}_{1}^{2}$
(B) $\mathrm{W}_{2}=0.33 \mathrm{~W}_{1}$
(C) $\mathrm{W}_{2}=\mathrm{W}_{1}$
(D) $\mathrm{W}_{2}=3 \mathrm{~W}_{1}$

Narendra Kumar

Numerade Educator

Problem 425

A ball is released from the top of a tower. What is the ratio of work done by force of gravity in first, second and third second of the motion of the ball ? $\left[h_{\mathrm{n}} \alpha(2 \mathrm{n}-1)\right]$
(A) $1: 2: 3$
(B) $1: 4: 9$
(C) $1: 3: 5$
(D) $1: 5: 3$

Narendra Kumar

Numerade Educator

Problem 426

A spring of spring constant $10^{3} \mathrm{~N} / \mathrm{m}$ is stretched initially $4 \mathrm{~cm}$ from the unscratched position. How much the work required to stretched it further by another $5 \mathrm{~cm}$ ?
(A) $6.5 \mathrm{NM}$
(B) $2.5 \mathrm{NM}$
(C) $3.25 \mathrm{NM}$
(D) $6.75 \mathrm{NM}$

Narendra Kumar

Numerade Educator

Problem 427

The mass of a car is $1000 \mathrm{~kg}$. How much work is required to be done on it to make it move with a speed of $36 \mathrm{~km} / \mathrm{h}$ ?
(A) $2.5 \times 10^{4} \mathrm{~J}$
(B) $5 \times 10^{3} \mathrm{~J}$
(C) $500 \mathrm{~J}$
(D) $5 \times 10^{4} \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 428

A body of mass $6 \mathrm{~kg}$ is under a force, which causes a displacement in it given by $\mathrm{S}=\left[\left(2 \mathrm{t}^{3}\right) / 3\right](\mathrm{in} \mathrm{m}) .$ Find the work done by the force in first one seconds.
(A) $2 \mathrm{~J}$
(B) $3.8 \mathrm{~J}$
(C) $5.2 \mathrm{~J}$
(D) $24 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 429

A $8 \mathrm{~kg}$ mass moves along $\mathrm{x}-$ axis. Its accelerations as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $\mathrm{x}=0$ to $\mathrm{x}=6 \mathrm{~cm}$ ?
(A) $48 \times 10^{-3} \mathrm{~J}$
(B) $98 \times 10^{-3} \mathrm{~J}$
(C) $4.8 \times 10^{-3} \mathrm{~J}$
(D) $9.8 \times 10^{-3} \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 430

The work done by a force acting on a body is as shown in the graph. What is the total work done in covering an initial distance of $15 \mathrm{~m}$ ?
(A) $50 \mathrm{~J}$
(B) $75 \mathrm{~J}$
(C) $100 \mathrm{~J}$
(D) $25 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 431

A spring gun of spring constant $90 \times 10^{2} \mathrm{~N} / \mathrm{M}$ is compressed $4 \mathrm{~cm}$ by a ball of mass $16 \mathrm{~g}$. If the trigger is pulled, calculate the velocity of the ball.
(A) $60 \mathrm{~m} / \mathrm{s}$
(B) $3 \mathrm{~m} / \mathrm{s}$
(C) $90 \mathrm{~m} / \mathrm{s}$
(D) $30 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 432

A uniform chain of length $2 \mathrm{~m}$ is kept on a table such that a length of $50 \mathrm{~cm}$ hangs freely from the edge of the table. The total mass of the chain is $5 \mathrm{~kg}$. What is the work done in pulling the entire chain on the table. $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{2}\right)$
(A) $7.2 \mathrm{~J}$
(B) $3 \mathrm{~J}$
(C) $4.6 \mathrm{~J}$
(D) $120 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 433

A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, the work required to pull the hanging part on to the table is
(A) MgL
(B) $[(\mathrm{MgL}) /(3)]$
(C) $[(\mathrm{MgL}) /(9)]$
(D) $[(\mathrm{MgL}) /(18)]$

Narendra Kumar

Numerade Educator

Problem 434

A cord is used to lower vertically a block of mass $\mathrm{M}$ by a distance $\mathrm{d}$ with constant downward acceleration $(9 / 2)$. Work done by the cord on the block is
(A) $-\mathrm{Mgd} / 2$
(B) $\mathrm{Mgd} / 4$
(C) $-3 \mathrm{Mgd} / 4$
(D) $\mathrm{Mgd}$

Narendra Kumar

Numerade Educator

Problem 435

A block of mass $5 \mathrm{~kg}$ is resting on a smooth surface. At what angle a force of $20 \mathrm{~N}$ be acted on the body so that it will acquired a kinetic energy of $40 \mathrm{~J}$ after moving $4 \mathrm{~m}$
(A) $30^{\circ}$
(B) $45^{\circ}$
(C) $60^{\circ}$
(D) $120^{\circ}$

Narendra Kumar

Numerade Educator

Problem 436

Natural length of a spring is $60 \mathrm{~cm}$, and its spring constant is $2000 \mathrm{~N} / \mathrm{m}$. A mass of $20 \mathrm{~kg}$ is hung from it. The extension produced in the spring is..... $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $4.9 \mathrm{~cm}$
(B) $0.49 \mathrm{~cm}$
(C) $9.8 \mathrm{~cm}$
(D) $0.98 \mathrm{~cm}$

Narendra Kumar

Numerade Educator

Problem 437

The potential energy of a body is given by $\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}$ (where $\mathrm{x}$ is displacement). The magnitude of force acting on the particle is
(A) constant
(B) proportional to $\mathrm{x}$
(C) proportional to $\mathrm{x}^{2}$
(D) Inversely proportional to $\mathrm{x}$

Narendra Kumar

Numerade Educator

Problem 438

A uniform chain of length $\mathrm{L}$ and mass $\mathrm{M}$ is lying on a smooth table and $(1 / 4)^{\text {th }}$ of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, the work required to pull the hanging part on to the table is
(A) MgL
(B) $\mathrm{MgL} / 9$
(C) $\mathrm{MgL} / 18$
(D) $\mathrm{MgL} / 32$

Narendra Kumar

Numerade Educator

Problem 439

If Wa, Wb, and Wc represent the work done in moving a particle from $\mathrm{X}$ to $\mathrm{Y}$ along three different path $\mathrm{a}, \mathrm{b}$, and $\mathrm{c}$ respectively (as shown) in the gravitational field of a point mass $\mathrm{m}$, find the correct relation between $\mathrm{Wa}, \mathrm{Wb}$ and $\mathrm{Wc}$
(A) $\mathrm{Wb}>\mathrm{Wa}>\mathrm{Wc}$
(B) $\mathrm{Wa}<\mathrm{Wb}<\mathrm{Wc}$
(C) $\mathrm{Wa}>\mathrm{Wb}>\mathrm{Wc}$
(D) $\mathrm{Wa}=\mathrm{Wb}=\mathrm{Wc}$

Narendra Kumar

Numerade Educator

Problem 440

An open knife edge of mass $\mathrm{m}$ is dropped from a height $\mathrm{h}$ on a wooden floor. If the blade penetrates up to the depth d into the wood, the average resistance offered by the wood to the knife edge is,
(A) $\mathrm{mg}$
(B) $\mathrm{mg}(1+\{\mathrm{h} / \mathrm{d}\})$
(C) $\mathrm{mg}(1+\{\mathrm{h} / \mathrm{d}\})^{2}$
(D) $m g(1-\{h / d\})$

Narendra Kumar

Numerade Educator

Problem 441

A toy car of mass $4 \mathrm{~kg}$ moves up a ramp under the influence of force $\mathrm{F}$ plotted against displacement $\mathrm{x}$. The maximum height attained is given by (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $\operatorname{ymax}=5 \mathrm{~m}$
(B) $\operatorname{ymax}=8 \mathrm{~m}$
(C) $\operatorname{ymax}=15 \mathrm{~m}$
(D) ymax $=20 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 442

A particle of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $\mathrm{v}=\mathrm{ax}^{3 / 2}$, Where $\mathrm{a}=5 \mathrm{~m}^{[(-1) / 2]} \mathrm{s}^{-1}$. The work done by the net
force during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=2 \mathrm{~m}$ is
(A) $50 \mathrm{~J}$
(B) $45 \mathrm{~J}$
(C) $25 \mathrm{~J}$
(D) None of these

Narendra Kumar

Numerade Educator

Problem 443

Velocity time graph of a particle of mass $2 \mathrm{~kg}$ moving in a straight line is as shown in figure. Work done by all forces on the particle is
(A) $400 \mathrm{~J}$
(B) $-400 \mathrm{~J}$
(C) $-200 \mathrm{~J}$
(D) $200 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 444

A mass of $\mathrm{M} \mathrm{kg}$ is suspended by a weight-less string, the horizontal force that is required to displace it until the string makes an angle of $60^{\circ}$ with the initial vertical direction is
(A) $\mathrm{Mg} / \sqrt{3}$
(B) $\mathrm{Mg} \cdot \sqrt{2}$
(C) $\mathrm{Mg} / \sqrt{2}$
(D) $\mathrm{Mg} \cdot \sqrt{3}$

Narendra Kumar

Numerade Educator

Problem 445

Given below is a graph between a variable force (F) (along $\mathrm{y}$ -axis) and the displacement $(\mathrm{X})$ (along $\mathrm{x}$ -axis) of a particle in one dimension. The work done by the force in the displacement interval between $0 \mathrm{~m}$ and $30 \mathrm{~m}$ is
(A) $275 \mathrm{~J}$
(B) $325 \mathrm{~J}$
(C) $400 \mathrm{~J}$
(D) $300 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 446

Force $\mathrm{F}$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12 \mathrm{~m}$.
(A) $27 \mathrm{~J}$
(B) $24 \mathrm{~J}$
(C) $36 \mathrm{~J}$
(D) $26 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 447

A force $F=A y^{2}+B y+C$ acts on a body in the $y$ -direction. The work done by this force during a displacement from $\mathrm{y}=-\mathrm{a}$ to $\mathrm{y}=\mathrm{a}$ is
(A) $\left[\left\{2 \mathrm{Aa}^{3}\right\} / 3\right]$
(B) $\left[\left\{2 \mathrm{Aa}^{3}\right\} / 3\right]+2 \mathrm{ca}$
(C) $\left[\left\{2 \mathrm{Aa}^{3}\right\} / 3\right]+\left[\left\{\mathrm{Ba}^{2}\right\} / 2\right]+\mathrm{ca}$
(D) None of these.

Narendra Kumar

Numerade Educator

Problem 448

A spring with spring constant $\mathrm{K}$ when stretched through $2 \mathrm{~cm}$ the potential energy is $\mathrm{U}$. If it is stretched by $6 \mathrm{~cm}$. The potential energy will be......
(A) $6 \mathrm{U}$
(B) $3 \mathrm{U}$
(C) $9 \mathrm{U}$
(D) $18 \mathrm{U}$

Narendra Kumar

Numerade Educator

Problem 449

If linear momentum of body is increased by $1.5 \%$, its kinetic energy increases by...... $\%$
(A) $0 \%$
(B) $10 \%$
(C) $2.25 \%$
(D) $3 \%$

Narendra Kumar

Numerade Educator

Problem 450

With what velocity should a student of mass $40 \mathrm{~kg}$ run so that his kinetic energy becomes $160 \mathrm{~J}$ ?
(A) $4 \mathrm{~m} / \mathrm{s}$
(B) $\sqrt{8} \mathrm{~m} / \mathrm{s}$
(C) $16 \mathrm{~m} / \mathrm{s}$
(D) $8 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 451

A body of mass $1 \mathrm{~kg}$ is thrown upwards with a velocity $20 \mathrm{~m} / \mathrm{s}$. It momentarily comes to rest after a height $18 \mathrm{~m}$. How much energy is lost due to air friction. $(\mathrm{g}=10 \mathrm{~m} / \mathrm{s} 2)$
(A) $20 \mathrm{~J}$
(B) $30 \mathrm{~J}$
(C) $40 \mathrm{~J}$
(D) $10 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 452

Two bodies of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. If $P_{1}$ and $P_{2}$ are their respective momentum, what is ratio of $\mathrm{P}_{2}: \mathrm{P}_{1}$ ?
(A) $\mathrm{m}_{1}: \mathrm{m}_{2}$
(B) $\sqrt{\mathrm{m}}_{2} / \sqrt{\mathrm{m}_{1}}$
(C) $\sqrt{m_{1}}: \sqrt{m_{2}}$
(D) $\mathrm{m}_{1}^{2}: \mathrm{m}_{2}^{2}$

Narendra Kumar

Numerade Educator

Problem 453

A body having a mass of $0.5 \mathrm{~kg}$ slips along the wall of a semispherical smooth surface of radius $20 \mathrm{~cm}$ shown in figure. What is the velocity of body at the bottom of the surface $?\left(\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $2 \mathrm{~m} / \mathrm{s}$
(B) $2 \mathrm{~m} / \mathrm{s}$
(C) $2 \sqrt{2} \mathrm{~m} / \mathrm{s}$
(D) $4 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 454

Two bodies of masses $\mathrm{m}$ and $3 \mathrm{~m}$ have same momentum. their respective kinetic energies $E_{1}$ and $E_{2}$ are in the ratio.....
(A) $1: 3$
(B) $3: 1$
(C) $1: 3$
(D) $1: 6$

Narendra Kumar

Numerade Educator

Problem 455

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $18 \mathrm{~cm}$ (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $0.4 \mathrm{~m} / \mathrm{s}$
(B) $4 \mathrm{~m} / \mathrm{s}$
(C) $1.8 \mathrm{~m} / \mathrm{s}$
(D) $0.6 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 456

A particle is placed at the origin and a force $\mathrm{F}=\mathrm{kx}$ is acting on it $($ Where $\mathrm{K}$ is positive constant) If $\mathrm{U}(\mathrm{o})=0$, which one of the following graph of $\mathrm{U}(\mathrm{x})$ versus $\mathrm{x}$. (where $\mathrm{U}$ is the potential energy function)

Narendra Kumar

Numerade Educator

Problem 457

A force $\rightarrow$ time graph for a linear motion is shown in figure where the segments are circular. What is linear momentum gained between zero and 8 second?
(A) $-2 \pi \mathrm{NS}$
(B) $0 \mathrm{NS}$
(C) $4 \pi \mathrm{NS}$
(D) $-6 \pi \mathrm{NS}$

Narendra Kumar

Numerade Educator

Problem 458

A particle is dropped from a height-h. A constant horizontal velocity is given to the particle. Taking $\mathrm{g}$ to be constant everywhere kinetic energy $\mathrm{E}$ of the particle with respect to time $t$ is correctly shown in....

Narendra Kumar

Numerade Educator

Problem 459

Which of the following graph is correct between kinetic energy (E), potential energy (U) and height (h) from the ground of the particle.

Narendra Kumar

Numerade Educator

Problem 463

A spring is compressed by $1 \mathrm{~cm}$ by a force of $4 \mathrm{~N}$. Find the potential energy of the spring when it is compressed by $10 \mathrm{~cm}$
(A) $2 \mathrm{~J}$
(B) $0.2 \mathrm{~J}$
(C) $20 \mathrm{~J}$
(D) $200 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 464

When $2 \mathrm{~kg}$ mass hangs to a spring of length $50 \mathrm{~cm}$, the spring stretches by $2 \mathrm{~cm}$. The mass is pulled down until the length of the spring becomes $60 \mathrm{~cm}$. What is the amount of elastic energy stored in the spring in this condition, if $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$
(A) $10 \mathrm{~J}$
(B) $2 \mathrm{~J}$
(C) $2.5 \mathrm{~J}$
(D) $5 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 465

The potential energy of a projectile at its highest point is (1/2) th the value of its initial kinetic energy. Therefore its angle of projection is
(A) $30^{\circ}$
(B) $45^{\circ}$
(C) $60^{\circ}$
(D) $75^{\circ}$

Narendra Kumar

Numerade Educator

Problem 466

Two bodies $\mathrm{P}$ and $\mathrm{Q}$ have masses $5 \mathrm{~kg}$ and $20 \mathrm{~kg}$ respectively. Each one is acted upon by a force of $4 \mathrm{~N}$. If they acquire the same kinetic energy in times $t_{\mathrm{P}}$ and $\mathrm{t}_{\mathrm{Q}}$ then the ratio $\left(t_{q} / t_{p}\right)=\ldots \ldots$
$(\mathrm{A})(1 / 2)$
(B) 2
(C) 5
(D) 6

Narendra Kumar

Numerade Educator

Problem 467

A particle of mass $0.1 \mathrm{~kg}$ is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at $\mathrm{x}=0$. What is the particle's velocity square at $\mathrm{x}=6 \mathrm{~cm}$ ?
(A) $0(\mathrm{~m} / \mathrm{s})^{2}$
(B) $240 \sqrt{2}(\mathrm{~m} / \mathrm{s})^{2}$
(C) $240 \sqrt{3}(\mathrm{~m} / \mathrm{s})^{2}$
(D) $480(\mathrm{~m} / \mathrm{s})^{2}$

Narendra Kumar

Numerade Educator

Problem 468

The potential energy of $2 \mathrm{~kg}$ particle, free to move along $\mathrm{x}$ axis is given by $\mathrm{U}(\mathrm{X})=\left[\left\{\mathrm{x}^{4} / 4\right\}-\left\{\mathrm{x}^{2} / 2\right\}\right] \mathrm{J}$. If its mechanical
energy is $2 \mathrm{~J}$, its maximum speed is $\ldots \mathrm{m} / \mathrm{s}$
(A) $(3 / 2)$
(B) $\sqrt{2}$
(C) $(1 / \sqrt{2})$
(D) 2

Narendra Kumar

Numerade Educator

Problem 469

If the K.E. of a body is increased by $44 \%$, its momentum will increase by.......
(A) $20 \%$
(B) $22 \%$
(C) $2 \%$
(D) $120 \%$

Narendra Kumar

Numerade Educator

Problem 470

A bullet of mass $0.10 \mathrm{~kg}$ moving with a speed of $100 \mathrm{~m} / \mathrm{s}$ enters a wooden block and is stopped after a distance of $0.20 \mathrm{~m}$. What is the average resistive force exerted by the block on the bullet ?
(A) $2.5 \times 10^{2} \mathrm{~N}$
(B) $25 \mathrm{~N}$
(C) $25 \times 10^{2} \mathrm{~N}$
(D) $2.5 \times 10^{4} \mathrm{~N}$

Narendra Kumar

Numerade Educator

Problem 471

A simple pendulum is released from $A$ as shown in figure. If $10 \mathrm{~g}$ and $100 \mathrm{~cm}$ represent the mass of the bob and length of the pendulum. what is the gain in $\mathrm{K} . \mathrm{E}$. at $\mathrm{B}$ ? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $0.5 \mathrm{~J}$
(B) $5 \times 10^{-2} \mathrm{~J}$
(C) $5 \mathrm{~J}$
(D) $0.5 \times 10^{-3} \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 472

A rifle bullet loses $(1 / 10)^{\text {th }}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
(A) 5
(B) 10
(C) 11
(D) 20

Saman Zulfiqar

Numerade Educator

Problem 473

A sphere of mass $\mathrm{m}$ moving the velocity $\mathrm{v}$ enters a hanging bag of sand and stops. If the mass of the bag is $\mathrm{M}$ and it is raised by height $\mathrm{h}$, then the velocity of the sphere was
(A) $[\{\mathrm{m}+\mathrm{M}\} / \mathrm{m}] \sqrt{(2 \mathrm{gh})}$
(B) $(\mathrm{M} / \mathrm{m}) \sqrt{(} 2 \mathrm{gh})$
(C) $[\mathrm{m} /\{\mathrm{M}+\mathrm{m}\}] \sqrt{(2 \mathrm{gh})}$
(D) $(\mathrm{m} / \mathrm{M}) \sqrt{(2 \mathrm{gh})}$

Narendra Kumar

Numerade Educator

Problem 474

A particle is acted upon by a force $\mathrm{F}$ which varies with position $\mathrm{x}$ as shown in figure. If the particle at $\mathrm{x}=0$ has kinetic energy of $20 \mathrm{~J}$. Then the calculate the kinetic energy of the particle at $\mathrm{x}=16 \mathrm{~cm}$.
(A) $45 \mathrm{~J}$
(B) $30 \mathrm{~J}$
(C) $70 \mathrm{~J}$
(D) $135 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 475

A frictionless track 12345 ends in a circular loop of radius $R$. A body slides down the track from point 1 Which is $6 \mathrm{~cm}$. Maximum value of $R$ for the body to successfully complete the loop is
(A) $6 \mathrm{~cm}$
(B) $(15 / 4) \mathrm{cm}$
(C) $(5 / 12) \mathrm{cm}$
(D) $(12 / 5) \mathrm{cm}$

Narendra Kumar

Numerade Educator

Problem 476

If the water falls from a dam into a turbine wheel $19.6 \mathrm{~m}$ below, then the velocity of water at the turbine is $\ldots \ldots$ $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $9.8 \mathrm{~m} / \mathrm{s}$
(B) $19.6 \mathrm{~m} / \mathrm{s}$
(C) $39.2 \mathrm{~m} / \mathrm{s}$
(D) $98.0 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 477

A bomb of $12 \mathrm{~kg}$ divides in two parts whose ratio of masses is $1: 4 .$ If kinetic energy of smaller part is $288 \mathrm{~J}$, then momentum of bigger part in $\mathrm{kgm} / \mathrm{sec}$ will be
(A) 38
(B) 72
(C) 108
(D) Data is incomplete

Narendra Kumar

Numerade Educator

Problem 478

An ice-cream has a marked value of $700 \mathrm{kcal}$. How many kilo-watt-hour of energy will it deliver to the body as it is digested $(\mathrm{J}=4.2 \mathrm{~J} / \mathrm{cal})$
(A) $0.81 \mathrm{kwh}$
(B) $0.90 \mathrm{kwh}$
(C) $1.11 \mathrm{kwh}$
(D) $0.71 \mathrm{kwh}$

Narendra Kumar

Numerade Educator

Problem 479

A spherical ball of mass $15 \mathrm{~kg}$ stationary at the top of a hill of height $82 \mathrm{~m} .$ It slides down a smooth surface to the ground, then climbs up another hill of height $32 \mathrm{~m}$ and finally slides down to horizontal base at a height of $10 \mathrm{~m}$ above the ground. The velocity attained by the ball is
(A) $30 \sqrt{10 \mathrm{~m} / \mathrm{s}}$
(B) $10 \sqrt{30 \mathrm{~m} / \mathrm{s}}$
(C) $12 \sqrt{10} \mathrm{~m} / \mathrm{s}$
(D) $10 \sqrt{12} \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 480

A bomb of mass $10 \mathrm{~kg}$ explodes into 2 pieces of mass $4 \mathrm{~kg}$ and $6 \mathrm{~kg}$. The velocity of mass $4 \mathrm{~kg}$ is $1.5 \mathrm{~m} / \mathrm{s}$, the K.E. of mass $6 \mathrm{~kg}$ is .......
(A) $3.84 \mathrm{~J}$
(B) $9.6 \mathrm{~J}$
(C) $3.00 \mathrm{~J}$
(D) $2.5 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 481

A bomb of mass $3.0 \mathrm{~kg}$ explodes in air into two pieces of masses $2.0 \mathrm{~kg}$ and $1.0 \mathrm{~kg}$. The smaller mass goes at a speed of $80 \mathrm{~m} / \mathrm{s}$. The total energy imparted to the two fragments is
(A) $1.07 \mathrm{KJ}$
(B) $2.14 \mathrm{KJ}$
(C) $2.4 \mathrm{KJ}$
(D) $4.8 \mathrm{KJ}$

Narendra Kumar

Numerade Educator

Problem 482

The bob of simple pendulum (mass $\mathrm{m}$ and length 1 ) dropped from a horizontal position strike a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be
(A) $2 \mathrm{mg} 1$
(B) $\mathrm{mg} 1 / 2$
(C) $\mathrm{mg} 1$
(D) zero

Narendra Kumar

Numerade Educator

Problem 483

A gun fires a bullet of mass $40 \mathrm{~g}$ with a velocity of $50 \mathrm{~m} / \mathrm{s}$. Because of this the gun is pushed back with a velocity of $1 \mathrm{~m} / \mathrm{s}$. The mass of the gun is
(A) $1.5 \mathrm{~kg}$
(B) $3 \mathrm{~kg}$
(C) $2 \mathrm{~kg}$
(D) $2.5 \mathrm{~kg}$

Narendra Kumar

Numerade Educator

Problem 484

The decreases in the potential energy of a ball of mass $25 \mathrm{~kg}$ which falls from a height of $40 \mathrm{~cm}$ is
(A) $968 \mathrm{~J}$
(B) $100 \mathrm{~J}$
(C) $1980 \mathrm{~J}$
(D) $200 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 485

If a man increase his speed by $2 \mathrm{~m} / \mathrm{s}$, his $\mathrm{K} . \mathrm{E}$. is doubled, the original speed of the man is
(A) $(2+2 \sqrt{2}) \mathrm{m} / \mathrm{s}$
(B) $(2+\sqrt{2}) \mathrm{m} / \mathrm{s}$
(C) $4 \mathrm{~m} / \mathrm{s}$
(D) $(1+2 \sqrt{2}) \mathrm{m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 486

The potential energy of a conservative system is given by $\mathrm{U}(\mathrm{X})=\left(\mathrm{x}^{2}-5 \mathrm{x}\right) \mathrm{J}$. Then the equilibrium position is at...... (where $\mathrm{x}$ in $\mathrm{m}$ )
(A) $\mathrm{x}=1.5 \mathrm{~m}$
(B) $\mathrm{x}=2 \mathrm{~m}$
(C) $\mathrm{x}=2.5 \mathrm{~m}$
(D) $\mathrm{x}=5 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 487

The potential energy of a particle varies with distance $\mathrm{x}$ as shown in the graph. The force acting on the particle is zero at
(A) $C$
(B) $\mathrm{B}$
(C) $\mathrm{B}$ and $\mathrm{C}$
(D) $\mathrm{A}$ and $\mathrm{D}$

Narendra Kumar

Numerade Educator

Problem 488

A nucleus at rest splits into two nuclear parts having same density and radii in the ratio $1: 2$. Their velocities are in the ratio
(A) $2: 1$
(B) $4: 1$
(C) $6: 1$
(D) $8: 1$

Narendra Kumar

Numerade Educator

Problem 489

A body of mass $1.5 \mathrm{~kg}$ slide down a curved track which is quadrant of a circle of radius $0.75$ meter. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is $\ldots . .$ ( $g=10 \mathrm{~m} / \mathrm{s} 2$ )
(A) $3.87 \mathrm{~m} / \mathrm{s}$
(B) $2 \mathrm{~m} / \mathrm{s}$
(C) $1.5 \mathrm{~m} / \mathrm{s}$
(D) $0.387 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 490

A single conservative force $\mathrm{F}(\mathrm{x})$ acts on a $2.5 \mathrm{~kg}$ particle that moves along the $\mathrm{x}$ -axis. The potential energy $\mathrm{U}(\mathrm{x})$ is given by $\mathrm{U}(\mathrm{x})=\left[10+(\mathrm{x}-4)^{2}\right]$ where $\mathrm{x}$ is in meter. $\mathrm{At} \mathrm{x}=6.0 \mathrm{~m}$ the
particle has kinetic energy of $20 \mathrm{~J}$. what is the mechanical energy of the system?
(A) $34 \mathrm{~J}$
(B) $45 \mathrm{~J}$
(C) $48 \mathrm{~J}$
(D) $49 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 491

A body initially at rest undergoes one dimensional motion with constant acceleration. The power delivered to it at time $\mathrm{t}$ is proportional to.....
(A) $\mathrm{t}^{1 / 2}$
(B) $t$
(C) $\mathrm{t}^{3 / 2}$
(D) $\mathrm{t}^{2}$

Narendra Kumar

Numerade Educator

Problem 492

An electric motor develops $5 \mathrm{KW}$ of power. How much time will it take to lift a water of mass $100 \mathrm{~kg}$ to a height of $20 \mathrm{~m}$ ? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $4 \mathrm{sec}$
(B) $5 \mathrm{sec}$
(C) $8 \mathrm{sec}$
(D) $10 \mathrm{sec}$

Narendra Kumar

Numerade Educator

Problem 493

Bansi does a given amount of work in $30 \mathrm{sec}$. Jaimeen does the same amount of work .. in $15 \mathrm{sec}$. The ratio of the output power of Bansi to the Jaimeen is....
(A) $1: 1$
(B) $1: 2$
(C) $2: 1$
(D) $5: 3$

Narendra Kumar

Numerade Educator

Problem 494

A rope-way trolley of mass $1200 \mathrm{~kg}$ uniformly from rest to a velocity of $72 \mathrm{~km} / \mathrm{h}$ in $6 \mathrm{~s}$. What is the average power of the engine during this period in watt ? (Neglect friction)
(A) $400 \mathrm{~W}$
(B) $40,000 \mathrm{~W}$
(C) $24000 \mathrm{~W}$
(D) $4000 \mathrm{~W}$

Narendra Kumar

Numerade Educator

Problem 495

A body of mass $\mathrm{m}$ is accelerated uniformly from rest to a speed $\mathrm{v}$ in time $\mathrm{T}$. The instantaneous power delivered to the body in terms of time is given by.....
(A) $\left[\left\{\mathrm{mv}^{2}\right\} /\left\{\mathrm{T}^{2}\right\}\right] \cdot \mathrm{t}$
(B) $\left[\left\{\mathrm{mv}^{2}\right\} /\left\{\mathrm{T}^{2}\right\}\right] \cdot \mathrm{t}^{2}$
(C) $\left[\left\{\mathrm{mv}^{2}\right\} /\{2 \mathrm{~T}\}\right] \cdot \mathrm{t}$
(D) $\left[\left\{\mathrm{mv}^{2}\right\} /\left\{2 \mathrm{~T}^{2}\right\}\right] \cdot \mathrm{t}^{2}$

Narendra Kumar

Numerade Educator

Problem 496

$1 \mathrm{~kg}$ apple gives $25 \mathrm{KJ}$ energy to a monkey. How much height he can climb by using this energy if his efficiency is $40 \%$. (mass of monkey $=25 \mathrm{~kg}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $20 \mathrm{~m}$
(B) $4 \mathrm{~m}$
(C) $30 \mathrm{~m}$
(D) $40 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 497

A force of $(2 \mathrm{i} \wedge+3 j \wedge-\mathrm{k} \wedge) \mathrm{N}$ acts on a body for 5 second, produces a displacement of $(3 i \wedge+5 j \wedge+k \wedge)$. What was the power used?
(A) $4 \mathrm{~W}$
(B) $20 \mathrm{~W}$
(C) $21 \mathrm{~W}$
(D) $4.2 \mathrm{~W}$

Narendra Kumar

Numerade Educator

Problem 498

If the force $\mathrm{F}$ is applied on a body and it moves with a velocity $\mathrm{v}$, the power will be
(A) $\mathrm{Fv}$
(B) $(\mathrm{F} / \mathrm{V})$
(C) $(\mathrm{F} / \mathrm{V})^{2}$
(D) $\mathrm{Fv}^{2}$

Narendra Kumar

Numerade Educator

Problem 499

From an automatic gun a man fires 240 bullet per minute with a speed of $360 \mathrm{~km} / \mathrm{h}$. If each weighs $20 \mathrm{~g}$, the power of the gun is
(A) $400 \mathrm{~W}$
(B) $300 \mathrm{~W}$
(C) $150 \mathrm{~W}$
(D) $600 \mathrm{~W}$

Narendra Kumar

Numerade Educator

Problem 500

A body of mass $\mathrm{M}$ is moving with a uniform speed of $10 \mathrm{~m} / \mathrm{s}$ on frictionless surface under the influence of two forces $F_{1}$ and $F_{2}$. The net power of the system is $\mathrm{F}_{1} \rightarrow[\mathrm{M}] \leftarrow \mathrm{F}_{2}$
(A) $10 \mathrm{~F}_{1} \mathrm{~F}_{2} \mathrm{M}$
(B) $10\left(\mathrm{~F}_{1}+\mathrm{F}_{2}\right) \mathrm{M}$
(C) $\left(\mathrm{F}_{1}+\mathrm{F}_{2}\right) \mathrm{M}$
(D) Zero

Narendra Kumar

Numerade Educator

Problem 501

A coolie $2.0 \mathrm{~m}$ tall raises a load of $75 \mathrm{~kg}$ in 25 from the ground to his head and then walks a distance to $40 \mathrm{~m}$ in another 25 . The power developed by the coolie is $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $0.25 \mathrm{kw}$
(B) $0.50 \mathrm{kw}$
(C) $0.75 \mathrm{kw}$
(D) $1.00 \mathrm{kw}$

Narendra Kumar

Numerade Educator

Problem 502

A body is moved along a straight line by a machine delivering a constant power. The velocity gained by the body in time $t$ is proportional to.....
(A) $t^{(3 / 4)}$
(B) $t^{(3 / 2)}$
(C) $t^{(1 / 4)}$
(D) $t^{(1 / 2)}$

Narendra Kumar

Numerade Educator

Problem 503

The coefficient of restitution e for a perfectly elastic collision is
(A) 1
(B) 0
(C) $\infty$
(D) $-1$

Narendra Kumar

Numerade Educator

Problem 504

Two balls at same temperature collide. What is conserved
(A) Temperature
(B) velocity
(C) kinetic energy
(D) momentum

Narendra Kumar

Numerade Educator

Problem 505

A particle of mass $\mathrm{m}$ moving with horizontal speed $6 \mathrm{~m} / \mathrm{s}$ as shown in figure. If $m<<M$ then for one dimensional elastic collision, the speed of lighter particle after collision will be (A) $1 \mathrm{~m} / \mathrm{s}$ in original direction.
(B) $2 \mathrm{~m} / \mathrm{s}$ opposite to the original direction.
(C) $1 \mathrm{~m} / \mathrm{s}$ opposite to the original direction.
(D) $2 \mathrm{~m} / \mathrm{s}$ in original direction.

Narendra Kumar

Numerade Educator

Problem 506

A rubber ball is dropped from a height of $5 \mathrm{~m}$ on a planet where the acceleration due to gravity is not known. On bouncing, it rises to $1.8 \mathrm{~m}$. The ball losses its velocity on bouncing by a factor of
(A) $(16 / 25)$
(B) $(9 / 25)$
(C) $(3 / 5)$
(D) $(2 / 5)$

Narendra Kumar

Numerade Educator

Problem 507

Three objects $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are kept in a straight line on a frictionless horizontal surface. These have masses $\mathrm{m}, 2 \mathrm{~m}$ and $\mathrm{m}$ respectively. The object $\mathrm{A}$ moves towards $\mathrm{B}$ with a speed $9 \mathrm{~m} / \mathrm{s}$ and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with $\mathrm{C}$. All motion occur on the same straight line. Find final speed of the object $\mathrm{C}$
(A) $3 \mathrm{~m} / \mathrm{s}$
(B) $4 \mathrm{~m} / \mathrm{s}$
(C) $5 \mathrm{~m} / \mathrm{s}$
(D) $1 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 508

Two solid rubber balls $P$ and $Q$ having masses $200 \mathrm{~g}$ and $400 \mathrm{~g}$ respectively are moving in opposite directions with velocity of $\mathrm{P}$ equal to $0.3 \mathrm{~m} / \mathrm{s}$. After collision the two balls come to rest, then the velocity of $Q$ is
(A) $0.15 \mathrm{~m} / \mathrm{s}$
(B) $1.5 \mathrm{~m} / \mathrm{s}$
(C) $-0.15 \mathrm{~m} / \mathrm{s}$
(D) Zero

Narendra Kumar

Numerade Educator

Problem 509

A sphere collides with another sphere of identical mass. After collision, the two sphere move. The collision is inelastic. Then the angle between the directions of the two spheres is
(A) Different from $90^{\circ}$
(B) $90^{\circ}$
(C) $0^{\circ}$
(D) $45^{\circ}$

Narendra Kumar

Numerade Educator

Problem 510

A ball is allowed to fall from a height $20 \mathrm{~m}$. If there is $30 \%$ loss of energy due to impact, then after one impact ball will go up to
(A) $18 \mathrm{~m}$
(B) $16 \mathrm{~m}$
(C) $12 \mathrm{~m}$
(D) $14 \mathrm{~m}$

Narendra Kumar

Numerade Educator

Problem 511

If a skater of weight $4 \mathrm{~kg}$ has initial speed $4 \mathrm{~m} / \mathrm{s}$ and $2^{\text {nd }}$ one of weight $6 \mathrm{~kg}$ has $6 \mathrm{~m} / \mathrm{s}$. After collision, they have speed (couple) $6 \mathrm{~m} / \mathrm{s}$. Then the loss in $\mathrm{K} . \mathrm{E}$. is.....
(A) $48 \mathrm{~J}$
(B) zero
(C) $96 \mathrm{~J}$
(D) None of these

Narendra Kumar

Numerade Educator

Problem 512

A metal ball of mass $2 \mathrm{~kg}$ moving with a velocity of $36 \mathrm{~km} / \mathrm{h}$ has a head on collision with a stationary ball of mass $3 \mathrm{~kg}$. If after the collision, the two balls move together, the loss in kinetic energy due to collision is
(A) $40 \mathrm{~J}$
(B) $60 \mathrm{~J}$
(C) $100 \mathrm{~J}$
(D) $140 \mathrm{~J}$

Narendra Kumar

Numerade Educator

Problem 513

A neutron having mass of $1.67 \times 10^{-27} \mathrm{~kg}$ and moving at $10^{8} \mathrm{~m} / \mathrm{s}$ collides with a deuteron at rest and sticks to it. If the mass of the deuteron is $3.34 \times 10^{-27} \mathrm{~kg}$ then the speed of the combination is
(A) $3.33 \times 10^{7} \mathrm{~m} / \mathrm{s}$
(B) $3 \times 10^{5} \mathrm{~m} / \mathrm{s}$
(C) $33.3 \times 10^{7} \mathrm{~m} / \mathrm{s}$
(D) $2.98 \times 10^{5} \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 514

A mass of $100 \mathrm{~g}$ strikes the wall speed $5 \mathrm{~m} / \mathrm{s}$ at an angle as shown in figure and is rebounds with the same speed. If the contact time is $5 \times 10^{-3} \mathrm{sec}$, what is the force applied on the mass by the wall
(A) $100 \sqrt{3} \mathrm{~N}$ to right
(B) $100 \mathrm{~N}$ to right
(C) $100 \sqrt{3} \mathrm{~N}$ to left
(D) $100 \mathrm{~N}$ to left

Narendra Kumar

Numerade Educator

Problem 515

Three identical spherical balls $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are placed on a table as shown in the figure along a straight line. $\mathrm{B}$ and $\mathrm{C}$ are at rest initially. The ball A hits B head on with a speed of $10 \mathrm{~m} / \mathrm{s}$. Then after all collision $\mathrm{A}$ and $\mathrm{B}$ are brought to rest and $\mathrm{C}$ takes off with velocity of $\ldots . .$ (elastic collision)
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $2.5 \mathrm{~m} / \mathrm{s}$
(C) $10 \mathrm{~m} / \mathrm{s}$
(D) $7.5 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 516

A ball dropped from a height of $4 \mathrm{~m}$ rebounds to a height of $2.4 \mathrm{~m}$ after hitting the ground. Then the percentage of energy lost is
(A) 40
(B) 50
(C) 30
(D) 600

Narendra Kumar

Numerade Educator

Problem 517

A billiard ball moving with a speed of $8 \mathrm{~m} / \mathrm{s}$ collides with an identical ball originally at rest. If the first ball stops after collision, then the second ball will move forward with a speed of .... (elastic collision)
(A) $8 \mathrm{~m} / \mathrm{s}$
(B) $4 \mathrm{~m} / \mathrm{s}$
(C) $16 \mathrm{~m} / \mathrm{s}$
(D) $1.0 \mathrm{~m} / \mathrm{s}$

Narendra Kumar

Numerade Educator

Problem 518

A bullet of mass $\mathrm{m}$ moving with velocity $\mathrm{v}$ strikes a block of mass $\mathrm{M}$ at rest and gets embedded into it. The kinetic energy of the composite block will be
(A) $(1 / 2) \mathrm{mv}^{2} \times[\mathrm{M} /(\mathrm{m}+\mathrm{m})]$
(B) $(1 / 2) \mathrm{mv}^{2} \times[(\mathrm{m}+\mathrm{m}) / \mathrm{M}]$
(C) $(1 / 2) \mathrm{MV}^{2} \times[\mathrm{m} /(\mathrm{m}+\mathrm{M})]$
(D) $(1 / 2) \mathrm{mv}^{2} \times[\mathrm{m} /(\mathrm{m}+\mathrm{M})]$

Narendra Kumar

Numerade Educator

Problem 519

A body of mass $\mathrm{m}_{1}$ is moving with a velocity $\mathrm{v}$. It collides with another stationary body of mass $\mathrm{m}_{1}$. They get embedded. At the point of collision, the velocity of the system
(A) Increases
(B) Decreases but does not become zero
(C) Remains same
(D) Become zero

Narendra Kumar

Numerade Educator

Problem 520

Two small particles of equal masses start moving in opposite directions from a point. A in a horizontal circular orbit. Their tangential velocities are $\mathrm{v}$ and $2 \mathrm{v}$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $\mathrm{A}$, these two particles will again reach the point $A$
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 521

Four identical balls are lined in a straight grove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide elastically with the row of 4 balls from left. What will happen
(A) One ball from the right rolls out with a speed $2 \mathrm{v}$ and the remaining balls will remain at rest.
(B) Two balls from the right roll out speed $\mathrm{v}$ each and the remaining balls will remain stationary.
(C) All the four balls in the row will roll out with speed $\mathrm{v}(\mathrm{v} / 4)$ each and the two colliding balls will come to rest.
(D) The colliding balls will come to rest and no ball rolls out from right.

Narendra Kumar

Numerade Educator

Problem 522

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: In the elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason: In the elastic collision the linear momentum of the system is conserved.
(A)1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 523

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: When a gas is allowed to expand, work done by gas is positive. Reason: Force due to gaseous pressure and displacement (of position) on in the same direction.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 524

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion : A light body and heavy body have same momentum. Then they also have same kinetic energy. Reason: Kinetic energy does not depend on mass of the body.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 525

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: Mountain roads rarely go straight up the slope. Reason: slope of mountains are large, therefore, more chances of vehicle to slip from roads.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 526

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: The change in kinetic energy of a particle is equal to the work done on it by the net force. Reason: Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 527

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: Work done in moving a body over a closed loop is zero for every force in nature. Reason: Work done does not depend on nature of force.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 528

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: A weight lifter does no work in holding the weight up. Reason: Work done is zero because distance moved is zero.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 529

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: stopping distance $=[\{$ Kinetic energy $\} /\{$ Stopping force $\}]$ Reason: Work done in stopping a body is equal to K.E. of the body.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 530

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: The mass equivalent of 1000 kwh energy is 40 microgram. Reason: This follows from $E=m c^{2}$ where $C=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 531

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: Work done by centripetal force is zero. Reason: This is because centripetal force is always along the tangent.
(A)1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 532

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion : Two bodies of different masses have same momentum. Their kinetic energy are in the inverse ratio of their masses. Reason $: \mathrm{K} . \mathrm{E} .=(1 / 2) \mathrm{mv}^{2}$
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 533

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion : Linear momentum is conserved in both, elastic and inelastic collisions. Reason: Total energy is conserved in all such collisions.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 534

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it.
(1) If both assertion and reason and the reason is the correct explanation of the Assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If the assertion is true but reason is false.
(4) If the assertion and reason both are false. Assertion: Both, a stretched spring and a compressed spring have potential energy. Reason: Work is done against the restoring force in each case.
(A) 1
(B) 2
(C) 3
(D) 4

Saman Zulfiqar

Numerade Educator

Problem 535

A force $\mathrm{F}=\mathrm{kx}$ (where $\mathrm{k}$ is positive constant) is acting on a particle. Match column-I and column-II, regarding work done in displacing the particle.
$$
\begin{array}{|l|l|}
\hline \text { Column - i } & \text { Column - ii } \\
\hline \text { (a) From } \mathrm{x}=-4 \text { to } \mathrm{x}=-2 & \text { (P) Positive } \\
\hline \text { (b) From } \mathrm{x}=-2 \text { to } \mathrm{x}=-4 & \text { (Q) zero } \\
\hline \text { (c) From } \mathrm{x}=-2 \text { to } \mathrm{x}=+2 & \text { (R) negative } \\
\hline
\end{array}
$$
(A) $\mathrm{a}-\mathrm{R}, \mathrm{b}-\mathrm{P}, \mathrm{c}-\mathrm{Q}$
(B) $a-P, b-Q, c-R$
(C) $a-R, b-Q, c-P$
(D) $\mathrm{a}-\mathrm{Q}, \mathrm{b}-\mathrm{P}, \mathrm{c}-\mathrm{R}$

Narendra Kumar

Numerade Educator

Problem 536

A body falls freely under the action of gravity from a height $\mathrm{h}$ above the ground.
$$
\begin{array}{|l|l|}
\hline \text { Column - i } & \text { Column - ii } \\
\hline \text { (a) P.E. }=2 \text { (K.E.) } & \text { (P) constant at every point } \\
\hline \text { (b) P.E. }=\text { K.E. } & \text { (Q) at height }(\mathrm{h} / 3) \\
\hline \text { (c) P.E. }=(1 / 2) \text { (K.E.) } & \text { (R) at height }(2 \mathrm{~h} / 3) \\
\hline \text { (d) P.E.+ K.E. } & \text { (S) at height }(\mathrm{h} / 2) \\
\hline
\end{array}
$$
(A) $a-P, b-Q, c-R, d-S$
(B) $\mathrm{a}-\mathrm{Q}, \mathrm{b}-\mathrm{P}, \mathrm{c}-\mathrm{S}, \mathrm{d}-\mathrm{R}$
(C) $\mathrm{a}-\mathrm{S}, \mathrm{b}-\mathrm{R}, \mathrm{c}-\mathrm{Q}, \mathrm{d}-\mathrm{P}$
(D) $\mathrm{a}-\mathrm{R}, \mathrm{b}-\mathrm{S}, \mathrm{c}-\mathrm{Q}, \mathrm{d}-\mathrm{P}$

Saman Zulfiqar

Numerade Educator

Problem 537

Two vehicles moving on a horizontal road are stopped by same retarding force.
$$
\begin{array}{|l|l|}
\hline \text { Column - i } & \text { Column - ii } \\
\hline \begin{array}{l}
\text { (a) When they have } \\
\text { same K.E. }
\end{array} & \begin{array}{l}
\text { (P) faster body stop in } \\
\text { larger distance }
\end{array} \\
\hline \begin{array}{l}
\text { (b) When they have different masses } \\
\text { but same velocity }
\end{array} & \begin{array}{l}
\text { (Q) larger body stops in } \\
\text { larger distance. }
\end{array} \\
\hline \begin{array}{l}
\text { (c) When both have same } \\
\text { momentum }
\end{array} & \begin{array}{l}
\text { (R) heavier body stops in } \\
\text { lighter distance. }
\end{array} \\
\hline \begin{array}{l}
\text { (d) When both have same } \\
\text { mass but different velocities }
\end{array} & \text { (S) stopped in same distance. } \\
\hline
\end{array}
$$
(A) $a-P, b-Q, c-R, d-S$
(B) $a-Q, b-P, c-S, d-R$
(C) $a-S, b-R, c-Q, d-P$
(D) $a-R, b-S, c-Q, d-P$

Saman Zulfiqar

Numerade Educator

Problem 560

An engine pump is used to pump a liquid of density $\rho$ continuously through a pipe of cross-sectional area $\mathrm{A}$. If the speed of flow of the liquid in the pipe is $\mathrm{v}$, then the rate at which kinetic energy is being imparted to the liquid is
(A) $(1 / 2) \mathrm{A} \rho \mathrm{V}^{3}$
(B) $(1 / 2) \mathrm{A} \rho \mathrm{V}^{2}$
(C) $(1 / 2) \mathrm{A} \rho \mathrm{V}$
(B) $\mathrm{ApV}$

Saman Zulfiqar

Numerade Educator

Problem 561

The velocity of a body of mass $400 \mathrm{gm}$ is $(-3 \mathrm{i} \wedge-4 \mathrm{j} \wedge) \mathrm{m} / \mathrm{s}$. So its kinetic energy is ......
(A) $5 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $8 \mathrm{~J}$
(D) $16 \mathrm{~J}$

Saman Zulfiqar

Numerade Educator

Problem 562

A particle is moving under the influence of a force given by $\mathrm{F}=\mathrm{kx}$, where $\mathrm{k}$ is a constant and $\mathrm{x}$ is the distance moved. What energy (in joule) gained by the particle in moving from $\mathrm{x}=1 \mathrm{~m}$ to $\mathrm{x}=3 \mathrm{~m} ?$
(A) $2 \mathrm{k}$
(B) $3 \mathrm{k}$
(C) $4 \mathrm{k}$
(D) $9 \mathrm{k}$

Saman Zulfiqar

Numerade Educator