JEE Main > Work, Energy and Power

Explore popular questions from Work, Energy and Power for JEE Main. This collection covers Work, Energy and Power previous year JEE Main questions hand picked by popular teachers.


Q 1.    

Correct4

Incorrect-1

Consider the following two statements:
A. Linear momentum of a system of particles is zero
B. Kinetic energy of a system of particles is zero. Then

A

A does not imply B and B does not imply A

B

A implies B but B does not imply A

A does not imply B but B implies A

D

A implies B and B implies A

Explanation


Q 2.    

Correct4

Incorrect-1

A wire suspended vertically from one of its ends is stretched by attaching a weight of {tex}200 \mathrm { N } {/tex} to the lower end. The weight stretches the wire by {tex}1 \mathrm { mm } {/tex} . Then the elastic energy stored in the wire is

A

{tex}0.2 \mathrm { J } {/tex}

B

{tex}10 \mathrm { J } {/tex}

C

{tex}20 \mathrm { J } {/tex}

{tex} 0.1\mathrm J {/tex}

Explanation

Q 3.    

Correct4

Incorrect-1

A spring of spring constant {tex} 5 \times 10 ^ { 3 } \mathrm { N } / \mathrm { m } {/tex} is stretched initially by 5{tex} \mathrm { cm } {/tex} from the unstretched position. Then the work required to stretch it further by another 5{tex} \mathrm { cm } {/tex} is

A

{tex} 12.50 \mathrm { N } - \mathrm { m } {/tex}

{tex} 18.75 \mathrm { N } - \mathrm { m } {/tex}

C

{tex} 25.00 \mathrm { N } - \mathrm { m } {/tex}

D

{tex} 6.25 \mathrm { N } - \mathrm { m } {/tex}

Explanation


Q 4.    

Correct4

Incorrect-1

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time {tex} 't '{/tex} is proportional to

A

{tex} t ^ { 3 / 4 } {/tex}

{tex} t ^ { 3 / 2 } {/tex}

C

{tex} t ^ { 1 / 4 } {/tex}

D

{tex} t ^ { 1 / 2 } {/tex}

Explanation


Q 5.    

Correct4

Incorrect-1

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement {tex} x {/tex} is proportional to

A

{tex} x {/tex}

B

{tex} e ^ { x } {/tex}

{tex} x ^ { 2 } {/tex}

D

{tex} \log _ { e } x {/tex}

Explanation

Q 6.    

Correct4

Incorrect-1

A uniform chain of length 2{tex} \mathrm { m } {/tex} is kept on a table such that a length of 60{tex} \mathrm { cm } {/tex} hangs freely from the edge of the table. The total mass of the chain is 4{tex} \mathrm { kg } {/tex} . What is the work done in pulling the entire chain on the table?

A

{tex}12 \mathrm { J } {/tex}

{tex}3.6 \mathrm { J } {/tex}

C

{tex}7.2 \mathrm { J } {/tex}

D

{tex}1200 \mathrm { J } {/tex}

Explanation

Q 7.    

Correct4

Incorrect-1

A force {tex} \vec { F } = ( 5 \vec { i } + 3 \vec { j } + 2 \vec { k } ) N {/tex} is applied over a particle which displaces it from its origin to the point {tex} \vec { r } = ( 2 \vec { i } - \vec { j } ) m . {/tex} The work done on the particle in joules is

A

{tex} + 10 {/tex}

{tex} + 7 {/tex}

C

{tex} - 7 {/tex}

D

{tex} + 13 {/tex}

Explanation

Q 8.    

Correct4

Incorrect-1

A body of mass {tex} {'m'} , {/tex} accelerates uniformly from rest to {tex}'v'_1 {/tex} in time {tex}'t'_1 . {/tex} The instantaneous power delivered to the body as a function of time {tex} 't'{/tex} is

A

{tex} \frac { m v _ { 1 } t ^ { 2 } } { t _ { 1 } } {/tex}

{tex} \frac { m v _ { 1 } ^ { 2 } t } { t _ { 1 } ^ { 2 } } {/tex}

C

{tex} \frac { m v _ { 1 } t } { t _ { 1 } } {/tex}

D

{tex} \frac { m v _ { 1 } ^ { 2 } t } { t _ { 1 } } {/tex}

Explanation

Q 9.    

Correct4

Incorrect-1

A Particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

its kinetic energy is constant

B

its acceleration is constant

C

its velocity is constant

D

it moves in a straight line

Explanation

Q 10.    

Correct4

Incorrect-1

The block of mass {tex} M {/tex} moving on the frictionless horizontal surface collides with the spring of spring constant {tex} k {/tex} and compresses it by length {tex} L {/tex} . The maximum momentum of the block after collision is

A

{tex} \frac { k L ^ { 2 } } { 2 M } {/tex}

{tex} \sqrt { M k } L {/tex}

C

{tex} \frac { M L ^ { 2 } } { k } {/tex}

D

zero

Explanation

Q 11.    

Correct4

Incorrect-1

A spherical ball of mass {tex}20\, \mathrm { kg } {/tex} is stationary at the top of a hill of height {tex}100\, \mathrm { m } {/tex} . It rolls down a smooth surface to the ground, then climbs up another hill of height {tex}30\, \mathrm { m } {/tex} and finally rolls down to a horizontal base at a height of {tex}20\, \mathrm { m } {/tex} above the ground. The velocity attained by the ball is

A

{tex}20 \mathrm { m } / \mathrm { s } {/tex}

{tex}40 \mathrm { m } / \mathrm { s } {/tex}

C

{tex}10 \sqrt { 30 } \mathrm { m } / \mathrm { s } {/tex}

D

{tex}10 \mathrm { m } / \mathrm { s } {/tex}

Explanation


Q 12.    

Correct4

Incorrect-1

A body of mass {tex} \mathrm { m } {/tex} is accelerated uniformly from rest to a speed {tex} \mathrm { v } {/tex} in a time {tex} T . {/tex} The instantaneous power delivered to the body as a function of time is given by

A

{tex} \frac { m v ^ { 2 } } { T ^ { 2 } }. t ^ { 2 } {/tex}

{tex} \frac { m v ^ { 2 } } { T ^ { 2 } }. t {/tex}

C

{tex} \frac { 1 } { 2 } \frac { m v ^ { 2 } } { T ^ { 2 } } .t ^ { 2 } {/tex}

D

{tex} \frac { 1 } { 2 } \frac { m v ^ { 2 } } { T ^ { 2 } }.t {/tex}

Explanation

Q 13.    

Correct4

Incorrect-1

A particle of mass {tex}100 \mathrm { g } {/tex} is thrown vertically upwards with a speed of {tex}5 \mathrm { m } / \mathrm { s } {/tex} . The work done by the force of gravity during the time the particle goes up is

A

{tex} - 0.5 \mathrm { J } {/tex}

{tex} - 1.25 \mathbf { J } {/tex}

C

{tex}1.25 \mathrm { J } {/tex}

D

{tex}0.5 \mathrm { J } {/tex}

Explanation

Q 14.    

Correct4

Incorrect-1

The potential energy of a 1{tex} \mathrm { kg } {/tex} particle free to move along the {tex} \mathrm { x } {/tex} -axis is given by {tex} V ( x ) = \left( \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 2 } } { 2 } \right) J {/tex}
The total mechanical energy of the particle is 2{tex} \mathrm { J } {/tex} . Then, the maximum speed (in m/s) is

{tex} \frac { 3 } { \sqrt { 2 } } {/tex}

B

{tex} \sqrt { 2 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 2 } } {/tex}

D

{tex}2{/tex}

Explanation


Q 15.    

Correct4

Incorrect-1

A 2 kg block slides on a horizontal floor with a speed of 4{tex} \mathrm { m } / \mathrm { s } {/tex} . It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is {tex}15 \mathrm { N } {/tex} and spring constant is {tex} 10,000 \mathrm { N } / \mathrm { m } {/tex} . The spring compresses by

A

{tex}8.5 \mathrm { cm } {/tex}

{tex} 5.5\mathrm { cm } {/tex}

C

{tex}2.5 \mathrm { cm } {/tex}

D

{tex}11.0 \mathrm { cm } {/tex}

Explanation

Q 16.    

Correct4

Incorrect-1

An athlete in the olympic games covers a distance of 100{tex} \mathrm { m } {/tex} in 10 s. His kinetic energy can be estimated to be in the range

A

{tex} 200 \mathrm { J } - 500 \mathrm { J } {/tex}

B

{tex} 2 \times 10 ^ { 5 } \mathrm {J} - 3 \times 10 ^ { 5 } \mathrm { J } {/tex}

C

{tex} 20,000 \mathrm { J } - 50,000 \mathrm { J } {/tex}

{tex} 2,000 \mathrm { J } - 5,000 \mathrm { J } {/tex}

Explanation

Q 17.    

Correct4

Incorrect-1

A block of mass {tex}0.50 \mathrm { kg } {/tex} is moving with a speed of {tex}2.00\, \mathrm { ms } ^ { - 1 } {/tex} on a smooth surface. It strikes another mass of {tex}1.00 \mathrm { kg } {/tex} and then they move together as a single body. The energy loss during the collision is

A

{tex} 0.16\mathrm J {/tex}

B

{tex} 1.00 \mathrm { J } {/tex}

{tex}0.67 \mathrm { J } {/tex}

D

{tex}0.34 \mathrm { J } {/tex}

Explanation


Q 18.    

Correct4

Incorrect-1

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by {tex} U ( x ) = \frac { a } { x ^ { 12 } } - \frac { b } { x ^ { 6 } } , {/tex} where a and b are constants and {tex} x {/tex} is the distance between the atoms. If the dissociation energy of the molecule is {tex} D = \left[ U ( x = \infty ) - U _ { \text {at equilibrium } } \right] , D {/tex} is

A

{tex} \frac { b ^ { 2 } } { 2 a } {/tex}

B

{tex} \frac { b ^ { 2 } } { 12 a } {/tex}

{tex} \frac { b ^ { 2 } } { 4 a } {/tex}

D

{tex} \frac { b ^ { 2 } } { 6 a } {/tex}

Explanation


Q 19.    

Correct4

Incorrect-1

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} of force constants {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } {/tex} , respectively, are stretched by the same force, it is found that more work is done on spring {tex} S _ { 1 } {/tex} than on spring {tex} S _ { 2 } {/tex} .
STATEMENT {tex} 1 : {/tex} If stretched by the same amount work done on {tex} \mathrm { S } _ { 1 } , {/tex} Work done on {tex} \mathrm { S } _ { 1 } {/tex} is more than {tex} \mathrm { S } _ { 2 } {/tex}
STATEMENT {tex} 2 : k _ { 1 } < k _ { 2 } {/tex}

Statement 1 is false, Statement 2 is true.

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1

D

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1

Explanation

Q 20.    

Correct4

Incorrect-1

When a rubber-band is stretched by a distance {tex} \mathrm { x } {/tex} , it exerts restoring force of magnitude {tex} \mathrm { F } = \mathrm { ax } + \mathrm { bx } ^ { 2 } {/tex} where a and b are constants. The work done in stretching the unstretched rubber-band by L is:

A

{tex} \mathrm { a L ^ { 2 } + b L ^ { 3 } }{/tex}

B

{tex} \mathrm { \frac { 1 } { 2 } \left( a L ^ { 2 } + b L ^ { 3 } \right)} {/tex}

{tex} \frac { \mathrm { aL } ^ { 2 } } { 2 } + \frac { \mathrm { bL } ^ { 3 } } { 3 } {/tex}

D

{tex} \frac { 1 } { 2 } \left( \frac { \mathrm { aL } ^ { 2 } } { 2 } + \frac { \mathrm { bL } ^ { 3 } } { 3 } \right) {/tex}

Explanation

Q 21.    

Correct4

Incorrect-1

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1{tex} \mathrm { m }\,\, 1000 {/tex} times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies {tex} 3.8 \times 10 ^ { 7 } \mathrm { J } {/tex} of energy per kg which is converted to mechanical energy with a 20{tex} \% {/tex} efficiency rate. Take g = 9.8 ms {tex} ^ { - 2 } : {/tex}

A

{tex} 9.89 \times 10 ^ { - 3 } \mathrm { kg } {/tex}

{tex} 12.89 \times 10 ^ { - 3 } \mathrm { kg } {/tex}

C

{tex} 2.45 \times 10 ^ { - 3 } \mathrm { kg } {/tex}

D

{tex} 6.45 \times 10 ^ { - 3 } \mathrm { kg } {/tex}

Explanation

Q 22.    

Correct4

Incorrect-1

A particle moves under the effect of a force {tex} F = C x {/tex} from {tex} x = 0 {/tex} to {tex} x = x _ { 1 } . {/tex} The work done in the process is

A

{tex} C x _ { 1 } ^ { 2 } {/tex}

{tex} \frac { 1 } { 2 } C x _ { 1 } ^ { 2 } {/tex}

C

{tex} C x _ { 1 } {/tex}

D

Zero

Explanation

Q 23.    

Correct4

Incorrect-1

A cord is used to lower vertically a block of mass {tex} M {/tex} by a distance {tex} d {/tex} with constant downward acceleration {tex} \frac { g } { 4 } . {/tex} Work done by the cord
on the block is

A

{tex} M g \frac { d } { 4 } {/tex}

B

{tex} 3 M g \frac { d } { 4 } {/tex}

{tex} - 3 M g \frac { d } { 4 } {/tex}

D

{tex} M g d {/tex}

Explanation







Q 24.    

Correct4

Incorrect-1

Two springs have their force constant as {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } \left( k _ { 1 } > k _ { 2 } \right) {/tex} When they are stretched by the same force

A

No work is done in case of both the springs

B

Equal work is done in case of both the springs

More work is done in case of second spring

D

More work is done in case of first spring

Explanation





Q 25.    

Correct4

Incorrect-1

A spring of force constant {tex} 10 \mathrm { N } / \mathrm { m } {/tex} has an initial stretch {tex} 0.20 \mathrm { m } {/tex}. In
changing the stretch to {tex} 0.25 \mathrm { m } {/tex}, the increase in potential energy is about

B

0.2 joule

C

{tex} {0.3} {/tex} joule

D

{tex} {0.5} {/tex} joule

Explanation