Work Energy and Power | Physics JEE previous year questions with Solutions

Q 1 :

A bullet of mass 50g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is [2024]

44%
32%
84%
16%

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(3)

$K_{i} = \frac{1}{2} m {(100)}^{2}$ and $K_{f} = \frac{1}{2} m {(40)}^{2}$

$% l o s s = \frac{| K_{f} - K_{i} |}{K_{i}} \times 100 = \frac{| \frac{1}{2} m {(40)}^{2} - \frac{1}{2} m {(100)}^{2} |}{\frac{1}{2} m {(100)}^{2}} \times 100$

$= \frac{| 1600 - 100 \times 100 |}{100} = 84 %$

Q 2 :

Four particles A, B, C, D of mass $\frac{m}{2}, m, 2 m, 4 m$ have same momentum, respectively. The particle with maximum kinetic energy is: [2024]

A
D
B
C

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(1)

Kinetic energy = $\frac{P^{2}}{2 m}$

$P \Rightarrow$ momentum (same for all)

$K E \propto \frac{1}{m a s s}$

Particle A is of least mass, has maximum kinetic energy

Q 3 :

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be [2024]

600%
500%
60%
6%

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(2)

Kinetic energy $(K) = \frac{P^{2}}{2 m} \Rightarrow P = \sqrt{2 m K}$

If $K_{f} = 36$ $K_{i} .$ So $P_{f} = 6$ $P_{i}$

% increase in momentum

$= \frac{P_{f} - P_{i}}{P_{i}} \times 100 % = \frac{6 P_{i} - P_{i}}{P_{i}} \times 100 % = 500 % \Rightarrow ∆ P % = 500 %$

Q 4 :

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

$1 : \sqrt{3} : 2$
$1 : \sqrt{3} : \sqrt{2}$
$\sqrt{3} : \sqrt{2} : 1$
$\sqrt{2} : \sqrt{3} : 1$

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(1)

$K_{A} = K_{B} = K_{C}$

Momentum $P = \sqrt{2 m K}$

$P \propto \sqrt{m}$

$P_{A} : P_{B} : P_{C} = \sqrt{m_{A}} : \sqrt{m_{B}} : \sqrt{m_{C}}$

$= \sqrt{400} : \sqrt{1200} : \sqrt{1600}$

$= 20 : 20 \sqrt{3} : 40$

$= 1 : \sqrt{3} : 2$

Q 5 :

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v = α \sqrt{x},$ where $α$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x = 0$ to $x = d,$ will be [2024]

$\frac{m}{2 α^{2} d}$
$\frac{m d}{2 α^{2}}$
$\frac{m α^{2} d}{2}$
$2 m α^{2} d$

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(3)

$v = α \sqrt{x}$

at $x = 0 : v = 0$ and at $x = d; v = α \sqrt{d}$

W.D. $= K_{f} - K_{i}$

W.D. $= \frac{1}{2} m {(α \sqrt{d})}^{2} - \frac{1}{2} m {(0)}^{2}$

$\Rightarrow$ W.D $= \frac{m α^{2} d}{2}$

Q 6 :

Two bodies of mass 4g and 25g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is [2024]

3 : 5
5 : 4
2 : 5
4 : 5

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(3)

$\frac{P_{1}^{2}}{2 m_{1}} = \frac{P_{2}^{2}}{2 m_{2}}$

$\frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \frac{2}{5}$

Q 7 :

An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

$\frac{M_{1}}{M_{1} + M_{2}}$
$\frac{M_{2}}{M_{1} + M_{2}}$
$\frac{M_{1}}{M_{2}}$
$\frac{M_{2}}{M_{1}}$

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(4)

$| \vec{p_{1}} | = | \vec{p_{2}} |$

$K E = \frac{p^{2}}{2 M} \Rightarrow$ $K E \propto \frac{1}{m}$

$\frac{K E_{1}}{K E_{2}} = \frac{p^{2} / 2 M_{1}}{p^{2} / 2 M_{2}} = \frac{M_{2}}{M_{1}}$

Q 8 :

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively [2025]

$\frac{S}{2}, \sqrt{\frac{3 g S}{2}}$
$\frac{S}{2}, \frac{3 g S}{2}$
$\frac{S}{4}, \frac{3 g S}{2}$
$\frac{S}{4}, \sqrt{\frac{3 g S}{2}}$

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(4)

Let height above the surface of earth be x,

$v^{2} = 0 + 2 g (S - x) = 2 g (S - x)$ ... (i)

The potential energy at a height x from the surface of earth,

U = mgx ... (ii)

$3 m g x = \frac{1}{2} m v^{2} \Rightarrow 3 g x = \frac{1}{2} \times 2 g (S - x)$

$4 x = S \Rightarrow x = \frac{S}{4}$

$\Rightarrow V = \sqrt{2 g \times \frac{3 S}{4}} = \sqrt{\frac{3 g S}{2}}$

Q 9 :

A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be [2023]

1 : 2
1 : 4
4 : 1
4 : 3

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(4)

$\frac{K E_{pop}}{K E_{top}} = \frac{\frac{1}{2} M {(u)}^{2}}{\frac{1}{2} M {(u \cos 30 °)}^{2}} = \frac{4}{3}$

Q 10 :

Given below are two statements: [2023]

Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.

Statement II: A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.

In the light of given statements, choose the most appropriate answer from the options given below.

Statement I is correct but Statement II is incorrect
Statement I is incorrect but Statement II is correct
Both Statement I is correct but Statement II are incorrect
Both Statement I is incorrect but Statement II are correct

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(1)

$Work done = Δ K E$

$Work done = - F S = 0 - K$

$S = \frac{K}{F}, Hence statement 1 is correct.$

[IMAGE 37]-------------------------------

$\vec{Δ V} = {\vec{V}}_{f} - {\vec{V}}_{i}$

$Velocity is changing \Rightarrow \vec{a} \neq 0$

Topic Question Set

Q 1 :

A bullet of mass 50g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is [2024]

Q 2 :

Four particles A, B, C, D of mass $\frac{m}{2}, m, 2 m, 4 m$ have same momentum, respectively. The particle with maximum kinetic energy is: [2024]

Q 3 :

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be [2024]

Q 4 :

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

Q 5 :

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v = α \sqrt{x},$ where $α$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x = 0$ to $x = d,$ will be [2024]

Q 6 :

Two bodies of mass 4g and 25g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is [2024]

Q 7 :

An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

Q 8 :

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively [2025]

Q 9 :

A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be [2023]

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