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

Q 1 :

A force $(3 x^{2} + 2 x - 5) N$ displaces a body from $x = 2 m$ to $x = 4 m .$ Work done by this force is __________ J. [2024]

(58) $Force, F = (3 x^{2} + 2 x - 5) N, x_{1} = 2 m$ $a n d$ $x_{2} = 4 m$

$Work done, W = \int_{x_{1}}^{x_{2}} F \cdot d x = \int_{2}^{4} (3 x^{2} + 2 x - 5) d x$

$W = {[x^{3}]}_{2}^{4} + {[x^{2}]}_{2}^{4} - 5 {[x]}_{2}^{4} = [64 - 8] + [16 - 4] - 5 [4 - 2] = 58 J$

Q 2 :

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be [2024]

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

1

2

3

4

(4)

Work done by gravity is path independent, it depends only on vertical displacement, so same work is done in both paths.

Q 3 :

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is [2024]

1 m
$\sqrt{6}$ m
$\sqrt{5}$ m
2 m

1

2

3

4

(4)

$\sin 30 ° = \frac{h}{10} \Rightarrow h = 5$

At maximum compression

using Work-Energy Theorem,

$W_{gravity} + W_{friction} + W_{spring} = Δ K E$

$m g h - μ m g (2 + x) - \frac{1}{2} k x^{2} = 0 - 0$

$5 \times 10 \times 5 - \frac{1}{2} \times 5 \times 10 (2 + x) - \frac{1}{2} 100 \times x^{2} = 0$

$250 - 50 x^{2} - [50 + 25 x] = 0$

$200 - 50 x^{2} - 25 x = 0$

$2 x^{2} + x - 8 = 0$

$x = \frac{- 1 \pm \sqrt{1^{2} + 4 \times 2 \times 8}}{2 \times 2} \Rightarrow x = \frac{- 1 \pm \sqrt{65}}{4} \approx 1.77 m$

Nearest answer is 2m.

Q 4 :

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is [2024]

4200
3900
4000
4500

1

2

3

4

(3)

Given $m = 100 k g,$ $μ = 0.4$

Friction force, $f = μ m g = 0.4 \times 100 \times 10 = 400 N$

Now $W = f \cdot s = 400 \times 10 = 4000 J$

Q 5 :

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60 by a force of 10 N parallel to the inclined surface as shown in the figure. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is $[g = 10 m / s^{2}]$ [2024]

$5 \sqrt{3}$ J
5 J
$5 \times 10^{3}$ J
10 J

1

2

3

4

(2)

$f_{k} = μ_{k} N = μ_{k} m g \cos 60 °$

$f_{k} = 0.1 \times 10 \times \frac{1}{2} = 0.5 N$

$W_{friction} = - f_{k} \cdot S$

$= - (0.5) \times 10$

$W_{friction} = - 5 J$

Q 6 :

A force $\vec{F} = 2 \hat{i} + b \hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2 \hat{j} - \hat{k}$ . What will be the value of b, if work done on the particle is zero. [2025]

0
$\frac{1}{2}$
$\frac{1}{3}$
2

1

2

3

4

(2)

Given, W = 0

$∴ \vec{F} \cdot \vec{S} = 0$

$(2 \hat{i} + b \hat{j} + \hat{k}) \cdot (\hat{i} - 2 \hat{j} - \hat{k}) = 0$

$2 - 2 b - 1 = 0 \Rightarrow b = \frac{1}{2}$

Q 7 :

A force $F = α + β x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $α$ = 1 N then $β$ will be [2025]

$15 N / m^{2}$
$10 N / m^{2}$
$12 N / m^{2}$
$8 N / m^{2}$

1

2

3

4

(3)

$F = α + β x^{2}$

Work done $\int d W = \int F \cdot d x$

$\Rightarrow △ W = \int F \cdot d x = \int (α + β x^{2}) d x$

$\Rightarrow △ W =$ $| α x + \frac{β x^{3}}{3} |_{0}^{1}$ $= α + \frac{β}{3} = 5$

Given $α$ = 1

So, $\frac{β}{3} = 4 \Rightarrow β = 12 N / m^{2}$

Q 8 :

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45° with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is: [2025]

970 J
735 J
245 J
490 J

1

2

3

4

(3)

$N = m g - \frac{F}{\sqrt{2}}$

Block travels with uniform velocity

$\frac{F}{\sqrt{2}} = μ [mg - \frac{F}{\sqrt{2}}]$

$\frac{F}{\sqrt{2}} = 0.25 [25 \times 9.8 - \frac{F}{\sqrt{2}}]$

$\Rightarrow 1.25 \frac{F}{\sqrt{2}} = 61.25$

$\Rightarrow F = \frac{61.25 \times \sqrt{2}}{1.25} = 49 \sqrt{2} N$

$W_{ext} = F S \cos 45 ° = 49 \sqrt{2} \times 5 \times \frac{1}{\sqrt{2}} = 245 J$ .

Q 9 :

A force $f = x^{2} y \hat{i} + y^{2} \hat{j}$ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

(152)

y = 10 – x

$W = \int_{0}^{4} x^{2} (10 - x) d x + \int_{0}^{2} y^{2} d y$

$= {[\frac{10 x^{3}}{3} - \frac{x^{4}}{4}]}_{0}^{4} + {[\frac{y^{3}}{3}]}_{0}^{2} = \frac{640}{3} - 64 + \frac{8}{3} = 152$ .

Q 10 :

Identify the correct statements from the following: [2023]

(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.

(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

(C) Work done by friction on a body sliding down an inclined plane is positive.

(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

(E) Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

B and E only
A and C only
B, D and E only
B and D only

1

2

3

4

(1)

B. Work done by gravitation will be negative if something is lifted upward.

E. Work done by air resistance is negative.

Q 11 :

A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N .$ The value of work done will be _________ J. [2023]

(40)

$W = \vec{F} ({\vec{r}}_{f} - {\vec{r}}_{i})$

$= (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot [(5 \hat{i} - 2 \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} - 4 \hat{k})]$

$W = 40 J$

Q 12 :

A force $F = (5 + 3 y^{2})$ acts on a particle in the $y$ -direction, where F is newton and $y$ is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is _______ J. [2023]

(132)

$F = 5 + 3 y^{2}$

$W = \int_{2}^{5} (5 + 3 y^{2}) d y = {[5 y + \frac{3 y^{3}}{3}]}_{2}^{5} = 132 J$

Q 13 :

A force $\vec{F} = (2 + 3 x) \hat{i}$ acts on a particle in the $x$ -direction, where $F$ is in newton and $x$ is in meter. The work done by this force during a displacement from $x$ = 0 to $x$ = 4 m, is __________ J. [2023]

(32)

$W = \int_{2}^{4} (2 + 3 x) d x$ $= {[2 x + \frac{3 x^{2}}{2}]}_{0}^{4} = 8 + 3 \times 8 = 32 J$

Q 14 :

A block of mass 10 kg is moving along $x$ -axis under the action of force $F = 5 x N .$ The work done by the force in moving the block from $x$ = 2 m to $x$ = 4 m will be ________ J. [2023]

(30)

$Work done = \int F d x$

$\int_{2}^{4} 5 x d x = 5 {[\frac{x^{2}}{2}]}_{2}^{4} = \frac{5}{2} [16 - 4] = 30 J$

Q 15 :

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 {m/s}^{2}, β = 1 m/s, γ = 1 m$ . The work done on the body during the time interval $t = 2$ s to $t = 3$ s is ______ J. [2026]

42
49
12
24

1

2

3

4

(4)

$x (t) = t^{2} + t + 1$

$v (t) = 2 t + 1$

$a (t) = 2$

$F = 4 N$

$Displacement = x (3) - x (2)$

$= 13 - 7 = 6 m$

$W = F \cdot S = 4 \times 6 = 24 J$

Topic Question Set

Q 1 :

A force $(3 x^{2} + 2 x - 5) N$ displaces a body from $x = 2 m$ to $x = 4 m .$ Work done by this force is __________ J. [2024]

Q 2 :

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be [2024]

Q 3 :

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is [2024]

Q 4 :

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is [2024]

Q 6 :

A force $\vec{F} = 2 \hat{i} + b \hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2 \hat{j} - \hat{k}$ . What will be the value of b, if work done on the particle is zero. [2025]

Q 7 :

A force $F = α + β x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $α$ = 1 N then $β$ will be [2025]

Q 9 :

A force $f = x^{2} y \hat{i} + y^{2} \hat{j}$ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

Q 11 :

A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N .$ The value of work done will be _________ J. [2023]

Q 12 :

A force $F = (5 + 3 y^{2})$ acts on a particle in the $y$ -direction, where F is newton and $y$ is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is _______ J. [2023]

Q 13 :

A force $\vec{F} = (2 + 3 x) \hat{i}$ acts on a particle in the $x$ -direction, where $F$ is in newton and $x$ is in meter. The work done by this force during a displacement from $x$ = 0 to $x$ = 4 m, is __________ J. [2023]

Q 14 :

A block of mass 10 kg is moving along $x$ -axis under the action of force $F = 5 x N .$ The work done by the force in moving the block from $x$ = 2 m to $x$ = 4 m will be ________ J. [2023]

Q 15 :

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 {m/s}^{2}, β = 1 m/s, γ = 1 m$ . The work done on the body during the time interval $t = 2$ s to $t = 3$ s is ______ J. [2026]

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Topic Question Set

Q 1 : A force (3x2+2x-5)N displaces a body from x=2m to x=4m. Work done by this force is __________ J. [2024]

Q 2 : A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be [2024]

Q 3 : A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is [2024]

Q 4 : A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is [2024]

Q 5 : A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60 by a force of 10 N parallel to the inclined surface as shown in the figure. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is [g=10m/s2] [2024]

Q 6 : A force F→=2i^+bj^+k^ is applied on a particle and it undergoes a displacement i^–2j^–k^. What will be the value of b, if work done on the particle is zero. [2025]

Q 7 : A force F=α+βx2 acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant α = 1 N then β will be [2025]

Q 9 : A force f=x2yi^+y2j^ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

Q 11 : A small particle moves to position 5i^-2j^+k^ from its initial position 2i^+3j^-4k^ under the action of force 5i^+2j^+7k^N. The value of work done will be _________ J. [2023]

Q 12 : A force F=(5+3y2) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is _______ J. [2023]

Q 13 : A force F→=(2+3x)i^ acts on a particle in the x-direction, where F is in newton and x is in meter. The work done by this force during a displacement from x = 0 to x = 4 m, is __________ J. [2023]

Q 14 : A block of mass 10 kg is moving along x-axis under the action of force F=5x N. The work done by the force in moving the block from x = 2 m to x = 4 m will be ________ J. [2023]

Q 15 : A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t)=αt2+βt+γm, where α=1 m/s2, β=1 m/s, γ=1 m . The work done on the body during the time interval t=2 s to t=3 s is ______ J. [2026]

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Q 1 :

A force $(3 x^{2} + 2 x - 5) N$ displaces a body from $x = 2 m$ to $x = 4 m .$ Work done by this force is __________ J. [2024]

Q 2 :

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be [2024]

Q 3 :

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is [2024]

Q 4 :

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is [2024]

Q 6 :

A force $\vec{F} = 2 \hat{i} + b \hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2 \hat{j} - \hat{k}$ . What will be the value of b, if work done on the particle is zero. [2025]

Q 7 :

A force $F = α + β x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $α$ = 1 N then $β$ will be [2025]

Q 9 :

A force $f = x^{2} y \hat{i} + y^{2} \hat{j}$ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

Q 11 :

A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N .$ The value of work done will be _________ J. [2023]

Q 12 :

A force $F = (5 + 3 y^{2})$ acts on a particle in the $y$ -direction, where F is newton and $y$ is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is _______ J. [2023]

Q 13 :

A force $\vec{F} = (2 + 3 x) \hat{i}$ acts on a particle in the $x$ -direction, where $F$ is in newton and $x$ is in meter. The work done by this force during a displacement from $x$ = 0 to $x$ = 4 m, is __________ J. [2023]

Q 14 :

A block of mass 10 kg is moving along $x$ -axis under the action of force $F = 5 x N .$ The work done by the force in moving the block from $x$ = 2 m to $x$ = 4 m will be ________ J. [2023]

Q 15 :

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 {m/s}^{2}, β = 1 m/s, γ = 1 m$ . The work done on the body during the time interval $t = 2$ s to $t = 3$ s is ______ J. [2026]