Work, Energy and Power NEET PYQ | Chapter-wise Previous Year Questions

Q 1 :

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If $F_{A}$ and $F_{B}$ are the forces applied by the brakes on cars A and B, respectively, then the ratio $F_{A} / F_{B}$ is [2025]

$\frac{1}{3}$
$\frac{1}{2}$
$\frac{3}{2}$
$\frac{2}{3}$

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4

(4)

According to work - energy theorem,

Work done = change in kinetic energy

$W = Δ K E$

For car A, $W_{A} = {(K E)}_{A}$

$F_{A} S_{A} = {(K E)}_{A}$ ...(i)

Similarly for car B, $F_{B} S_{B} = {(K E)}_{B}$ ...(ii)

From eqn. (i) and (ii)

$\frac{{(K E)}_{A}}{{(K E)}_{B}} = \frac{F_{A} S_{A}}{F_{B} S_{B}} \Rightarrow \frac{100}{225} = \frac{F_{A}}{F_{B}} \times \frac{1000}{1500} \Rightarrow \frac{F_{A}}{F_{B}} = \frac{2}{3}$

Q 2 :

An object moving along horizontal $x$ -direction with kinetic energy 10 J is displaced through $\vec{x} = (3 \hat{i})$ $m$ , by the force $\vec{F} = (- 2 \hat{i} + 3 \hat{j})$ $N$ . The kinetic energy of the object at the end of the displacement $x$ is: [2024]

10 J
16 J
4 J
6 J

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4

(3)

Given, $\vec{F} = (- 2 \hat{i} + 3 \hat{j}) N$ or $\vec{x} = (3 \hat{i}) m$

Initial Kinetic energy, $(K_{i}) = 10 J$

$W = \vec{F} \cdot \vec{x} = (- 2 \hat{i} + 3 \hat{j}) \cdot (3 \hat{i}) = - 6 J$

Using work-energy theorem, $W = Δ K . E .$

$- 6 = K_{f} - K_{i} or - 6 = K_{f} - 10;$ $K_{f} = 4 J$

Q 3 :

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 ${ms}^{- 1}$ . Take $g$ constant with a value 10 ${ms}^{- 2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]

(i) 1.25 J (ii) - 8.25 J
(i) 100 J (ii) 8.75 J
(i) 10J (ii) - 8.75 J
(i) - 10J (ii) - 8.25 J

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(3)

Here, $m = 1$ $g = 10^{- 3}$ $kg,$

$h = 1 km = 1000 m, v = 50 {m s}^{- 1}, g = 10 {m s}^{- 2}$

(i) The work done by the gravitational force

$= m g h = 10^{- 3} \times 10 \times 1000 = 10 J$

(ii) The total work done by gravitational force and the resistive force of air is equal to change in kinetic energy of rain drop.

$∴$ $W_{g} + W_{r} = \frac{1}{2} m v^{2} - 0$

$10 + W_{r} = \frac{1}{2} \times 10^{- 3} \times 50 \times 50$ or $W_{r} = - 8.75 J$

Q 4 :

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{- 4}$ $J$ by the end of the second revolution after the beginning of the motion? [2016]

$0.18 {m/s}^{2}$
$0.2 {m/s}^{2}$
$0.1 {m/s}^{2}$
$0.15 {m/s}^{2}$

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(3)

Here, $m = 10$ $g = 10^{- 2} kg, R = 6.4 cm = 6.4 \times 10^{- 2} m,$

$K_{f} = 8 \times 10^{- 4} J, K_{i} = 0, a_{t} = ?$

Using work energy theorem,

Work done by all the forces = Change in KE

$W_{tangential force} + W_{centripetal force} = K_{f} - K_{i}$

$\Rightarrow a_{t} = \frac{K_{f}}{4 π R m} = \frac{8 \times 10^{- 4}}{4 \times \frac{22}{7} \times 6.4 \times 10^{- 2} \times 10^{- 2}} = 0.099 \approx 0.1 {ms}^{- 2}$

Topic Question Set

Q 1 :

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If $F_{A}$ and $F_{B}$ are the forces applied by the brakes on cars A and B, respectively, then the ratio $F_{A} / F_{B}$ is [2025]

Q 2 :

An object moving along horizontal $x$ -direction with kinetic energy 10 J is displaced through $\vec{x} = (3 \hat{i})$ $m$ , by the force $\vec{F} = (- 2 \hat{i} + 3 \hat{j})$ $N$ . The kinetic energy of the object at the end of the displacement $x$ is: [2024]

Q 3 :

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 ${ms}^{- 1}$ . Take $g$ constant with a value 10 ${ms}^{- 2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]

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Topic Question Set

Q 1 : The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If FA and FB are the forces applied by the brakes on cars A and B, respectively, then the ratio FA/FB is [2025]

Q 2 : An object moving along horizontal x-direction with kinetic energy 10 J is displaced through x→=(3i^)m, by the force F→=(-2i^+3j^)N. The kinetic energy of the object at the end of the displacement x is: [2024]

Q 3 : Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 ms-1. Take g constant with a value 10 ms-2. The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]

Q 4 : A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10-4J by the end of the second revolution after the beginning of the motion? [2016]

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Q 1 :

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If $F_{A}$ and $F_{B}$ are the forces applied by the brakes on cars A and B, respectively, then the ratio $F_{A} / F_{B}$ is [2025]

Q 2 :

An object moving along horizontal $x$ -direction with kinetic energy 10 J is displaced through $\vec{x} = (3 \hat{i})$ $m$ , by the force $\vec{F} = (- 2 \hat{i} + 3 \hat{j})$ $N$ . The kinetic energy of the object at the end of the displacement $x$ is: [2024]

Q 3 :

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 ${ms}^{- 1}$ . Take $g$ constant with a value 10 ${ms}^{- 2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]