Examples of Work Done

Q. The work done to raise a mass $m$ from the surface of the earth to a height $h$, which is equal to the radius of the earth is

1. $2mgR$
2. $\frac{3}{2}mgR$
3. $\frac{1}{2}mgR$
4. $mgR$

Q. A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius $R$ of the earth. The change in potential energy of the body will be -

1. $\frac{1}{3}mgR$
2. $2mgR$
3. $\frac{2}{3}mgR$
4. $3mgR$

Q. A body of mass $m$ is lifted from the surface of earth to a height equal to $R/3$, where $R$ is the radius of earth. Potential energy of the body increases by

1. $\frac{mgR}{3}$
2. $\frac{mgR}{4}$
3. $\frac{mgR}{5}$
4. $\frac{mgR}{9}$

Q. Four particles $\text{A, B, C}$ and $\text{D}$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $\text{D}$ is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $\text{D}$ during its movement is

1. $\frac{G{m}^2}{L}$
2. $\frac{2G{m}^2}{L}$
3. $\frac{G{m}^2}{L}\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
4. $-\frac{G{m}^2}{L}\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$

Q.

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

1. $\frac{m{v}^2}{r}\times \pi r$

2. $Zero$

3. $\frac{m{v}^2}{r^2}$

4. $\frac{\pi r^2}{m{v}^2}$

Q. The magnitude of potential energy per unit mass of an object at the surface of earth is $E$, the escape velocity of the object is

1. $\sqrt{2E}$
2. $4E^2$
3. $\sqrt{E}$
4. $2E$

Q. Two particles $\text{A}$ and $\text{B}$ each of mass $m$ are separated by a distance $r$. Another particle $\text{C}$ of mass $M$ is placed at the midpoint of $\text{A}$ and $\text{B}$. Find the work done in taking $\text{C}$ to a point at a distance $r$ from both $\text{A}$ and $\text{B}$ without acceleration.
$(G=$ Gravitational constant and only gravitational interaction between $\text{A, B}$ and $\text{C}$ is considered$)$

1. $\frac{GMm}{r}$
2. $\frac{2GMm}{r}$
3. $\frac{3GMm}{r}$
4. $\frac{4GMm}{r}$

Q. The variation of potential energy $U$ of a body moving along $x-$axis varies with its position $\left(x\right)$ as shown in figure
The body is in equilibrium state at:

1. A
2. B
3. C
4. Both A & C

Q.

A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

1. $100rJ$

2. $\left(\frac{r}{100}\right)J$

3. $\left(\frac{100}{r}\right)J$

4. Zero

Q. Assertion :In circular motion, work done by all the forces acting on the body is zero. Reason: Centripetal force and velocity are mutually perpendicular.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. The change in potential energy when a body of mass $m$ is raised to height $nR$ from the earth's surface is ($R$ is radius of earth)

1. $\Delta U=\left(\frac{n+1}{n}\right)\frac{GMm}{R}$
2. $\frac{GMm}{R}$
3. $\Delta U=\left(\frac{n}{n+1}\right)\frac{GMm}{R}$
4. $\Delta U=-\left(\frac{n}{n+1}\right)\frac{GMm}{R}$

Q. A uniform cable of mass ${}^{\prime }{M}^{\prime }$ and length ${}^{\prime }{L}^{\prime }$ is placed on a horizontal surface such that its ${\left(\frac{1}{n}\right)}^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

1. $\frac{MgL}{n^2}$
2. $nMgL$
3. $\frac{MgL}{2n^2}$
4. $\frac{2MgL}{n^2}$

Q. If $V$ is the gravitational potential on the surface of the earth, then what is its value at the centre of the earth?
(Assume that mass distribution is uniform)

1. $2V$
2. $3V$
3. $\frac{3}{2}V$
4. $\frac{2}{3}V$

Q. If a body of mass $m$ is sent to a height of $R/5$ from the earth surface, the potential energy increases by $(R\to$ radius of earth):-

1. $\frac{mgR}{6}$
2. $\frac{4}{5}mgR$
3. $\frac{5}{6}mgR$
4. $\frac{6}{7}mgR$

Q. Potential energy of an object raised through a height h is ________ ( 1/2 $m{v}^2$, mgh).

Q. If the temperature of the Sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on Earth to what it previously was, will be :

1. 4
2. 16
3. 32
4. 64

Q. Gravitational potential of the body of mass m at a height h from surface of earth of radius R is (Take $g=$ acceleration due to gravity at earth's surface)

1. $-g(R+h)$
2. $-g(R-h)$
3. $g(R+h)$
4. $g(R-h)$

Q. A person trying to lose weight by burning fat lifts a mass of $10\text{kg}$ upto a height of $1\text{m}$ for $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up, considering work is done only when the weight is lifted up? Fat supplies $3.8\times {10}^7\text{J/kg}$ which is converted to mechanical energy at an efficiency of $20$% . Take $g=9.8{\text{ms}}^{-2}$. Consider weight to be lifted slowly.

1. $9.89\times {10}^{-3}\text{kg}$
2. $12.89\times {10}^{-3}\text{kg}$
3. $2.45\times {10}^{-3}\text{kg}$
4. $6.45\times {10}^{-3}\text{kg}$

Q. Assertion :The strain present in the material after unloading is called the residual strain or plastic strain and the strain disappears during unloading is termed as recoverable or elastic strain. Reason: After yieild point, there is some residual stress left in an material on unloading.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A black body radiates energy at the rate of $E$ watt per metr$e^2$ at a high ternperature $T$ K. when the temperature is reduced to $\left(T/2\right)$ K, the radiant energy will be

1. $E/16$
2. $E/2$
3. $E/4$
4. $2E$

Q. The unit of (V) Gravitational Potential is

1. $\frac{\text{Joule}}{kg}$
2. $\text{Joule}$
3. $\frac{\text{Joule}}{s}$
4. $\frac{kg}{\text{Joule}}$

Q. A stone of mass 8 kg has been lifted to a height of 2 m from the ground. Calculate the rise in its potential energy.

1. 156.8 J
2. 165.8 J
3. 16 J
4. 160 J

Q. If $g$ is the acceleration due to gravity on earth's surface, the gain in potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is:

1. $mgR$
2. $2mgR$
3. $\left(1/4\right)mgR$
4. $\left(1/2\right)mgR$

Q. If a body of mass m has to be taken from the surface to the earth to a height h = R, then the amount of energy required is (R = radius of the earth)

1. $\frac{mgR}{3}$
2. $mgR$
3. $\frac{mgR}{2}$
4. $\frac{mgR}{12}$
5. $\frac{mgR}{9}$

Q. A body of density $\rho$ and volume $V$ is lifted through height $h$ in a liquid of density $\sigma (<\rho )$. Then increase in gravitational potential energy of the body is:

1. $V\sigma gh$
2. $V\rho gh$
3. $V(\rho -\sigma )gh$
4. Zero

Q. If $V_s$ is the gravitational potential on the surface of the earth, then what is its value at distance ${\left(\frac{1}{4}\right)}^{th}$ of the radius of the earth from the centre of the earth?
(Assume that mass distribution is uniform)

1. $\frac{49}{32}{V}_s$
2. $\frac{47}{32}{V}_s$
3. $\frac{23}{32}{V}_s$
4. $\frac{25}{32}{V}_s$

Q. A disc of mass $3m$ and a disc of mass $m$ are connected by a massless spring of stiffness $k$. The heavier disc is placed on the ground with the spring vertical and lighter disc on top. From its equilibrium position, the upper disc is pushed down by a distance $\delta$ and released. Then

1. if $\delta =2$mg/k, maximum normal reaction from ground on lower disc$=6$ mg.
2. if $\delta >3$mg/k the lower disc will bounce up
3. if $\delta =2$mg/k, maximum normal reaction from ground on lower disc $=4$ mg.
4. if $\delta >4$ mg/k the lower disc will bounce up

Q. A solid body $X$ of heat capacity $C$ is kept in an atmosphere whose temperature is $T_A=300K$. At time $t=0$ the temperature of $X$ is $T_0=400K$. It cools according to Newton's law of cooling. At time $t_1$ its temperature is found to be $350K$. At this time $t_1$ the body $X$ is connected to a larger body $Y$ at atmospheric temperature $T_A$ through conducting rod of length $L$ cross-sectional area $A$ and thermal conductivity $k$. The heat capacity of $Y$ is so large that any variation in its temperature may be neglected. The cross-sectional area $A$ of the connecting rod is small compared to the surface area of $X$. Find the temperature of $X$ at time $t=3t_1$.

1. $T=300+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
2. $T=400+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
3. $T=350+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
4. $T=300+60exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.

Q. A particle of mass $10\text{g}$ is kept on the surface of a uniform sphere of mass $100\text{kg}$ and radius $10\text{cm}$, find the work to be done against the gravitational force between them to take the particle for away from the sphere:-
$(G=6.67\times {10}^{-11}\frac{N{m}^2}{k{g}^2})$

1. $6.67\times {10}^{-9}\text{J}$
2. $6.67\times {10}^{-10}\text{J}$
3. $13.34\times {10}^{-10}\text{J}$
4. $3.33\times {10}^{-10}\text{J}$

Q. A 2-kg block is thrown upward from a point 20 m above earth's surface. At what height above earth's surface, the gravitational potential energy of the block is increased by 500 J?

1. 5 m
2. 25 m
3. 45 m
4. 70 m