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)

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

$v (t) = 2 t + 1$

$a (t) = 2$

$F = 4 N$

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

$= 13 - 7 = 6 m$

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

Q 16 :

Two springs have their force constant as $k_{1}$ and $k_{2}$ $(k_{1} > k_{2})$ . When they are stretched by the same force up to equilibrium:

No work is done by this force in case of both the springs
Equal work is done by this force in case of both the springs
More work is done by this force in case of second spring
More work is done by this force in case of first spring

1

2

3

4

(3)

$F_{1} = F_{2}$

$∵$ $w_{1} = \frac{1}{2} k_{1} x_{1}^{2},$ $k_{1} x_{1} = k_{2} x_{2} = F$

$w_{1} = \frac{1}{2} k_{1} {[\frac{F}{k_{1}}]}^{2} = \frac{1}{2} \frac{F^{2}}{k_{1}}$

$∴$ $w_{2} = \frac{1}{2} \frac{F^{2}}{k_{2}}$

$∵$ $k_{1} > k_{2}$

$∴$ $w_{1} < w_{2}$

Q 17 :

A particle undergoes from position O(0,0,0) to $A (a, 2 a, 0)$ via path $y = \frac{2 x^{2}}{a}$ in $x - y$ plane under the action of a force which varies with particle's $(x, y, z)$ coordinate as $\vec{F} = x^{2} y \hat{i} + y z^{2} e^{2 z} \hat{j} - (\frac{z}{x + 2 y}) \hat{k} .$ Work done by the force $\vec{F}$ is: (all symbols have their usual meaning and they are in SI unit.)

$\frac{4 a^{4}}{5}$
$\frac{a^{4}}{5}$
$\frac{a^{3}}{4}$
$\frac{2 a^{4}}{5}$

1

2

3

4

(4)

$\vec{F} = x^{2} y \hat{i} + y z^{2} e^{2 z} \hat{j} - (\frac{z}{x + 2 y}) \hat{k}$

$d \vec{r} = d x \hat{i} + d y \hat{j} + d z \hat{k}$

$d w = \vec{F} \cdot d \vec{r} = x^{2} y d x + y z^{2} e^{2 z} d y - (\frac{z}{x + 2 y}) d z$

$for the given path z = 0, y = \frac{2 x^{2}}{a}$

$d w = x^{2} y d x = \frac{2 x^{4}}{a} d x$

$W = \int d w = \frac{2}{a} \int_{0}^{a} x^{4} d x = \frac{2 a^{4}}{5}$

Q 18 :

Statement – I: Work done by friction on a body sliding down an inclined plane is always positive.

Statement – II: Work done is greater than zero, if angle between force and displacement is acute.

Both statement I and statement II are correct
Statement I is incorrect and statement II is correct
Statement I is correct and statement II is incorrect
Both statement I and statement II are incorrect

1

2

3

4

(2)

Work done by friction on inclined plane will be negative

$W = F s \cos θ = + v e, i f θ < 90 ° .$

Q 19 :

A mass of 1 kg kept in an inclined plane with $30 °$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is ______ J. (Take g = 10 ${m/s}^{2}$ ) [2026]

20
25
30
10

1

2

3

4

(1)

$f_{x} = m g \sin θ = 5 N$

[IMAGE 15]

$W = f_{s} (v t) \sin θ = 5 \times 4 \times 2 \times \frac{1}{2} = 20 N$

Q 20 :

A body of mass 1 kg moves along a straight line with a velocity $v = 2 x^{2}$ . The work done by the body during displacement from $x = 0$ to 5 m is ______ J. [2026]

0
250
1250
1000

1

2

3

4

(3)

$W = Δ K . E = K_{f} - K_{i}$

$W = \frac{1}{2} m (v_{f}^{2} - v_{i}^{2})$

$= \frac{1}{2} \times 1 {[(2 {{(5)}^{2})}^{2} - (2 {(0))}^{2}]}_{0}^{5}$

$= \frac{1}{2} \times 50 \times 50 = 1250 J$

Q 21 :

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 ${m/s}^{2}$ ). [2026]

[IMAGE 16]

7.74
7.20
6.55
4.50

1

2

3

4

(1)

[IMAGE 17]

$W_{G} = Δ K$

$m_{B} g h - m_{A} g h = \frac{1}{2} (m_{A} + m_{B}) v^{2}$

$(6 - 2) \times 10 \times 6 = \frac{1}{2} (8) v^{2}$

$\Rightarrow v = \sqrt{60} m / s = 7.746 m / s$

Q 22 :

A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) N$ and $(3 \hat{i} - \hat{j} - 2 \hat{k}) N$ is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is _______ J. [2026]

(35)

$\begin{matrix} {\vec{F}}_{1} = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) N \\ {\vec{F}}_{2} = (3 \hat{i} - \hat{j} - 2 \hat{k}) N \end{matrix}} \Rightarrow {\vec{F}}_{net} = (5 \hat{i} + 2 \hat{j} + 2 \hat{k}) N$

$(distance) d = 25 m along (3 \hat{i} - 4 \hat{j}) direction$

$∴$ $displacement \vec{d} = 25 (\frac{3 \hat{i} - 4 \hat{j}}{\sqrt{9 + 16}}) = 25 (\frac{3 \hat{i} - 4 \hat{j}}{5}) m$

$\vec{d} = (15 \hat{i} - 20 \hat{j}) m$

$So, work done W = {\vec{F}}_{net} \cdot \vec{d}$

$W = (5 \hat{i} + 2 \hat{j} + 2 \hat{k}) \cdot (15 \hat{i} - 20 \hat{j}) = 35 J$

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]

Q 16 :

Two springs have their force constant as $k_{1}$ and $k_{2}$ $(k_{1} > k_{2})$ . When they are stretched by the same force up to equilibrium:

Q 18 :

Statement – I: Work done by friction on a body sliding down an inclined plane is always positive.

Statement – II: Work done is greater than zero, if angle between force and displacement is acute.

Q 20 :

A body of mass 1 kg moves along a straight line with a velocity $v = 2 x^{2}$ . The work done by the body during displacement from $x = 0$ to 5 m is ______ J. [2026]

Q 21 :

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 ${m/s}^{2}$ ). [2026]

[IMAGE 16]

Q 22 :

A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) N$ and $(3 \hat{i} - \hat{j} - 2 \hat{k}) N$ is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process 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]

Q 16 : Two springs have their force constant as k1 and k2 (k1>k2). When they are stretched by the same force up to equilibrium:

Q 17 : A particle undergoes from position O(0,0,0) to A(a,2a,0) via path y=2x2a in x-y plane under the action of a force which varies with particle's (x,y,z) coordinate as F→=x2yi^+yz2e2zj^-(zx+2y)k^. Work done by the force F→ is: (all symbols have their usual meaning and they are in SI unit.)

Q 18 : Statement – I: Work done by friction on a body sliding down an inclined plane is always positive. Statement – II: Work done is greater than zero, if angle between force and displacement is acute.

Q 19 : A mass of 1 kg kept in an inclined plane with 30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is ______ J. (Take g = 10 m/s2) [2026]

Q 20 : A body of mass 1 kg moves along a straight line with a velocity v=2x2. The work done by the body during displacement from x=0 to 5 m is ______ J. [2026]

Q 21 : The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 m/s2). [2026] [IMAGE 16]

Q 22 : A 1 kg block subjected to two simultaneous forces (2i^+3j^+4k^) N and (3i^-j^-2k^) N is moved a distance of 25 m along (3i^-4j^) direction. The work done in this process 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]

Q 16 :

Two springs have their force constant as $k_{1}$ and $k_{2}$ $(k_{1} > k_{2})$ . When they are stretched by the same force up to equilibrium:

Q 18 :

Statement – I: Work done by friction on a body sliding down an inclined plane is always positive.

Statement – II: Work done is greater than zero, if angle between force and displacement is acute.

Q 20 :

A body of mass 1 kg moves along a straight line with a velocity $v = 2 x^{2}$ . The work done by the body during displacement from $x = 0$ to 5 m is ______ J. [2026]

Q 21 :

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 ${m/s}^{2}$ ). [2026]

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Q 22 :

A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) N$ and $(3 \hat{i} - \hat{j} - 2 \hat{k}) N$ is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is _______ J. [2026]