Work, Energy & Power · JEE Main previous year questions

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____. ($g$ is acceleration due to gravity at the surface of earth)

1. A.$\frac{1}{2}mg{R}_e$
2. B.$\frac{3}{4}mg{R}_e$
3. C.$\frac{1}{4}mg{R}_e$
4. D.$\frac{2}{3}mg{R}_e$

A copper wire of length $3\mathrm{m}$ is stretched by $3\mathrm{mm}$ by applying an external force. The volume of the wire is $600\times 10^{-6}{\mathrm{m}}^3$. The elastic potential energy stored in the wire in stretched condition would be ____ $\mathrm{J}$. (Given Young modulus of copper $=1.1\times 10^{11}N/{\mathrm{m}}^2$)

1. A.$X_1$
2. B.$X_2$
3. C.$X_3$
4. D.All the metals will give out photo electrons with same kinetic energies.

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

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ molecules, kept in two different sized containers are same, then their temperatures will be same. Reason R: The r.m.s. speed of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ molecules are same at same temperature. Choose the correct answer from the options given below

1. A.Both A and R are true and R is the correct explanation of A
2. B.Both A and R are true but R is NOT the correct explanation of A
3. C.A is true but R is false
4. D.A is false but R is true

If a body of mass $1\mathrm{kg}$ falls on the earth from infinity, it attains velocity ($v$) and kinetic energy ($k$) on reaching the surface of earth. The values of $v$ and $k$ respectively are ____. (Take radius of earth to be $6400\mathrm{km}$ and $g=9.8m/{\mathrm{s}}^2$)

1. A.$11.2km/s$; $6.27\times 10^7\mathrm{J}$
2. B.$11.2km/s$; $12.54\times 10^7\mathrm{J}$
3. C.$8.8km/s$; $6.27\times 10^7\mathrm{J}$
4. D.$8.8km/s$; $12.54\times 10^7\mathrm{J}$

1. A.$4E$
2. B.$2E$
3. C.$\frac{4}{3}E$
4. D.$3E$

A point charge of $10^{-8}\mathrm{C}$ is placed at origin. The work done in moving a point charge $2\mu \mathrm{C}$ from point $A(4,4,2)\mathrm{m}$ to $B(2,2,1)\mathrm{m}$ is ____ J. $\left(\frac{1}{4\pi {ϵ}_0}=9\times 10^9\text{ in SI units}\right)$

1. A.$30\times 10^{-6}$
2. B.0
3. C.$15\times 10^{-6}$
4. D.$45\times 10^{-6}$

A light wave described by $E=60\left[\sin \left(3\times 10^{15}\right)t+\sin \left(12\times 10^{15}\right)t\right]$ (in SI units) falls on a metal surface of work function $2.8\mathrm{eV}$ . The maximum kinetic energy of ejected photoelectron is (approximately) ____ eV. $\left(h=6.6\times 10^{-34}J.s.\text{ and }e=1.6\times 10^{-19}\mathrm{C}\right)$

1. A.3.8
2. B.7.8
3. C.6.0
4. D.5.1

1. A.$F_{BC}>F_{AB}>F_{DE}>F_{CD}$
2. B.$F_{BC}>F_{CD}>F_{DE}>F_{AB}$
3. C.$F_{CD}>F_{AB}>F_{BC}>F_{DE}$
4. D.$F_{CD}>F_{DE}>F_{AB}>F_{BC}$

A sample of a liquid is kept at $1\mathrm{atm}$. It is compressed to $5\mathrm{atm}$ which leads to a change of volume of $0.8{\mathrm{cm}}^3$. If the bulk modulus of the liquid is $2\mathrm{GPa}$, the initial volume of the liquid was $\underline{}$ litre. (Take $1\mathrm{atm}=10^5\mathrm{Pa}$)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2}\mathrm{mgR}$, where R is the radius of earth. Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the options given below

1. A.A is false but R is true
2. B.Both A and R are true and R is the correct explanation of A
3. C.A is true but R is false
4. D.Both A and R are true but R is NOT the correct explanation of A

A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

1. A.$\frac{S}{4},\frac{3gS}{2}$
2. B.$\frac{S}{2},\frac{3gS}{2}$
3. C.$\frac{S}{4},\sqrt{\frac{3gS}{2}}$
4. D.$\frac{S}{2},\sqrt{\frac{3gS}{2}}$

Two cylindrical vessels of equal cross sectional area of $2{\mathrm{m}}^2$ contain water upto heights $10\mathrm{m}$ and $6\mathrm{m}$, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^3{kg/m}^3$ and $g=10{m/s}^2$)

1. A.$1\times 10^5\mathrm{J}$
2. B.$4\times 10^4\mathrm{J}$
3. C.$8\times 10^4\mathrm{J}$
4. D.$6\times 10^4\mathrm{J}$

1. A.$0.3\mathrm{m}$
2. B.$0.1\mathrm{m}$
3. C.$0.4\mathrm{m}$
4. D.$0.2\mathrm{m}$

A sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{\mathrm{dm}}{\mathrm{dt}}\propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

1. A.$\mathrm{P}\propto \sqrt{\mathrm{v}}$
2. B.$\mathrm{P}\propto \mathrm{v}$
3. C.$P^2\propto v^3$
4. D.$P^2\propto v^5$

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below

1. A.$\mathbf{A}$ is false but $\mathbf{R}$ is true
2. B.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
3. C.$\mathbf{A}$ is true but $\mathbf{R}$ is false
4. D.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

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

1. A.$15N/{\mathrm{m}}^2$
2. B.$10N/{\mathrm{m}}^2$
3. C.$12N/{\mathrm{m}}^2$
4. D.$8N/{\mathrm{m}}^2$

The amount of work done to break a big water drop of radius ' $R$ ' into $27$ small drops of equal radius is $10\mathrm{J}$ . The work done required to break the same big drop into $64$ small drops of equal radius will be

1. A.$20\mathrm{J}$
2. B.$10\mathrm{J}$
3. C.$5\mathrm{J}$
4. D.$15\mathrm{J}$

1. A.
2. B.
3. C.
4. D.

A ball having kinetic energy $\mathrm{KE}$, is projected at an angle of $60^{\circ }$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

1. A.$\frac{(\mathrm{KE})}{2}$
2. B.$\frac{(\mathrm{KE})}{8}$
3. C.$\frac{(\mathrm{KE})}{4}$
4. D.$\frac{(\mathrm{KE})}{16}$

UV light of $4.13\mathrm{eV}$ is incident on a photosensitive metal surface having work function $3.13\mathrm{eV}$. The maximum kinetic energy of ejected photoelectrons will be:

1. A.$4.13\mathrm{eV}$
2. B.$1\mathrm{eV}$
3. C.$7.26\mathrm{eV}$
4. D.$3.13\mathrm{eV}$

The temperature of a gas is $-78^{\circ }\mathrm{C}$ and the average translational kinetic energy of its molecules is $\mathrm{K}$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2\mathrm{K}$ is :

1. A.$-78^{\circ }\mathrm{C}$
2. B.$127^{\circ }\mathrm{C}$
3. C.$-39^{\circ }\mathrm{C}$
4. D.$117^{\circ }\mathrm{C}$

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