Work Done by Forces

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JEE Main 2020

A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E_{0} (1 - a x^{2})$ in the x-direction, where $a$ and $E_{0}$ are constants. Initially, the particle was at rest at $x = 0$ . Other than the initial position, the kinetic energy of the particle becomes zero when the distance of the particle from the origin is

\frac{1}{a}

(B)

a

(C)

\frac{3}{a}

(D)

\frac{2}{a}

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Main

An engine is attached to a wagon through a shock absorber of length $1.5 m$ . The system with a total mass of $40000 kg$ is moving with a speed of $72 kmh^{- 1}$ , when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0 m$ . If $90%$ of energy of the wagon is lost due to friction, the spring constant is ......... $\times 1 0^{5} N/m$ .

JEE Main 2021, 27 Aug Shift-I

LEVELJEE Main

Two persons $A$ and $B$ perform same amount of work in moving a body through a certain distance $d$ with application of forces acting at angle $4 5^{\circ}$ and $6 0^{\circ}$ with the direction of displacement respectively. The ratio of force applied by person $A$ to the force applied by person $B$ is $\frac{1}{x}$ . The value of $x$ is ....... .

LEVELJEE Main

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by

This question has Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $S_{1}$ and $S_{2}$ of force constants $k_{1}$ and $k_{2}$ respectively are stretched by the same force, it is found that more work is done on spring $S_{1}$ than on spring $S_{2}$ . Statement I If stretched by the same amount, work done on $S_{1}$ will be more than that on $S_{2}$ . Statement II $k_{1} < k_{2}$

(A)

Statement I is false, Statement II is true

(B)

Statement I is true, Statement II is false

(C)

Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I

(D)

Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I

JEE Main 2020, 4 Sep Shift-II

LEVELJEE Main

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

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 particle takes place in a plane, it follows that

(A)

its velocity is constant

(B)

its acceleration is constant

(C)

its kinetic energy is constant

(D)

it moves in a straight line

LEVELJEE Main

A spring of spring constant $5 \times 1 0^{3}$ N/m is stretched initially by $5$ cm from the unstretched position. Then, the work required to stretch it further by another $5$ cm is

(A)

12.50

N-m

(B)

18.75

N-m

(C)

25.00

N-m

(D)

6.25

N-m

JEE Main 2020, 9 Jan Shift-I

LEVELJEE Main

Consider a force $F = - x \hat{i} + y \hat{j}$ . The work done by this force in moving a particle from point $A (1, 0)$ to $B (0, 1)$ along the line segment is (all quantities are in SI units)

(A)

\frac{3}{2}

(B)

(C)

(D)

\frac{1}{2}

LEVELJEE Main

A spring of force constant $800 N/m$ has an extension of $5 cm$ . The work done in extending it from $5 cm$ to $15 cm$ is

(A)

16 J

(B)

8 J

(C)

32 J

(D)

24 J

LEVELJEE Main

A mass of $M$ kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $4 5^{\circ}$ with the initial vertical direction is

(A)

M g (2 + 1)

(B)

M g 2

(C)

\frac{M g}{2}

(D)

M g (2 - 1)

JEE Main 2019, 10 Jan Shift-II

LEVELJEE Main

A particle which is experiencing a force, is given by $F = 3 \hat{i} - 12 \hat{j}$ , undergoes a displacement of $d = 4 \hat{i}$ . If the particle had a kinetic energy of $3 J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?

(A)

9 J

(B)

15 J

(C)

12 J

(D)

10 J

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

A force of $F = (5 y + 20) \hat{j} N$ acts on a particle. The work done by this force when the particle is moved from $y = 0 m$ to $y = 10 m$ is ...... J.

JEE Main 2020

LEVELJEE Main

A cricket ball of mass $0.15 kg$ is thrown vertically up by a bowling machine, so that it rises to a maximum height of $20 m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of $0.2 m$ , while launching the ball, the value of $F$ (in N) is (Take, $g = 10 ms^{- 2}$ ) ........... .

LEVELJEE Main

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

(A)

x^{2}

(B)

e^{x}

(C)

x

(D)

lo g_{e} x

LEVELJEE Main

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

(A)

7.2 J

(B)

3.6 J

(C)

120 J

(D)

1200 J

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Main

A body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 g h$ . The value of workdone by the air-friction is

(A)

- 0.68 m g h

(B)

m g h

(C)

1.64 m g h

(D)

0.64 m g h

LEVELJEE Main

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?

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

A block of mass $m$ lying on a smooth horizontal surface is attached to a spring (of negligible mass) of spring constant $k$ . The other end of the spring is fixed as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$ , the maximum speed of the block is

(A)

\frac{π F}{mk}

(B)

\frac{F}{mk}

(C)

\frac{2 F}{mk}

(D)

\frac{F}{π mk}

JEE Main 2019, 8 April Shift-I

LEVELJEE Main

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is

JEE Main 2019, 9 Jan Shift-II

LEVELJEE Main

A force acts on a 2 kg object, so that its position is given as a function of time as $x = 3 t^{2} + 5$ . What is the work done by this force in first 5 seconds?

JEE Main 2021, 22 July Shift-II

LEVELJEE Main

A porter lifts a heavy suitcase of mass $80 kg$ and at the destination lowers it down by a distance of $80 cm$ with a constant velocity. Calculate the work done by the porter in lowering the suitcase. [Take, $g = 9.8 ms^{- 2}$ ]

(A)

- 62720.0 J

(B)

- 627.2 J

(C)

+ 627.2 J

(D)

784.0 J

JEE Main 2016 (Offline)

LEVELJEE Main

A person trying to lose weight by burning fat lifts a mass of $10 kg$ upto a height of $1 m$ , $1000$ 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 $3.8 \times 1 0^{7} J$ of energy per kg which is converted into mechanical energy with a $20%$ of efficiency rate. (Take, $g = 9.8 ms^{- 2}$ )

(A)

2.45 \times 1 0^{- 3} kg

(B)

6.45 \times 1 0^{- 3} kg

(C)

9.89 \times 1 0^{- 3} kg

(D)

12.89 \times 1 0^{- 3} kg

JEE Main 2017

LEVELJEE Main

A time dependent force $F = 6 t$ acts on a particle of mass $1 kg$ . If the particle starts from rest, the work done by the force during the first $1 s$ will be

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by

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 particle takes place in a plane, it follows that

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A spring of spring constant 5×103 N/m is stretched initially by 5 cm from the unstretched position. Then, the work required to stretch it further by another 5 cm is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider a force F=−xi^+yj^​. The work done by this force in moving a particle from point A(1,0) to B(0,1) along the line segment is (all quantities are in SI units)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A force of F=(5y+20)j^​ N acts on a particle. The work done by this force when the particle is moved from y=0 m to y=10 m is ...... J.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body of mass m dropped from a height h reaches the ground with a speed of 0.8gh​. The value of workdone by the air-friction is

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A force F=(5i^+3j^​+2k^) N is applied over a particle which displaces it from its origin to the point r=(2i^−j^​) m. The work done on the particle in joule is

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A force acts on a 2 kg object, so that its position is given as a function of time as x=3t2+5. What is the work done by this force in first 5 seconds?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A time dependent force F=6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 s will be

A spring of spring constant $5 \times 1 0^{3}$ N/m is stretched initially by $5$ cm from the unstretched position. Then, the work required to stretch it further by another $5$ cm is

Consider a force $F = - x \hat{i} + y \hat{j}$ . The work done by this force in moving a particle from point $A (1, 0)$ to $B (0, 1)$ along the line segment is (all quantities are in SI units)

A spring of force constant $800 N/m$ has an extension of $5 cm$ . The work done in extending it from $5 cm$ to $15 cm$ is

A force of $F = (5 y + 20) \hat{j} N$ acts on a particle. The work done by this force when the particle is moved from $y = 0 m$ to $y = 10 m$ is ...... J.

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

A body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 g h$ . The value of workdone by the air-friction is

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

A force acts on a 2 kg object, so that its position is given as a function of time as $x = 3 t^{2} + 5$ . What is the work done by this force in first 5 seconds?

A time dependent force $F = 6 t$ acts on a particle of mass $1 kg$ . If the particle starts from rest, the work done by the force during the first $1 s$ will be