Work, Energy & Power · JEE Main previous year questions

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-

1. A.$t^{2/3}$
2. B.$t^{3/2}$
3. C.$t$
4. D.$t^{1/2}$

An object of mass $m_1$ collides with another object of mass $m_2$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_2:m_1$ is :

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

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below :

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

27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is __________ times that of a smaller drop.

Given below are two statements : Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false.
4. D.Statement I is false but Statement II is true.

If the potential energy between two molecules is given by $$U=-\frac{A}{r^6}+\frac{B}{r^{12}},$$ then at equilibrium, separation between molecules, and the potential energy are :

1. A.${\left(\frac{2B}{A}\right)}^{1/6},-\frac{A^2}{4B}$
2. B.${\left(\frac{2B}{A}\right)}^{1/6},-\frac{A^2}{2B}$
3. C.${\left(\frac{B}{A}\right)}^{1/6},0$
4. D.${\left(\frac{B}{2A}\right)}^{1/6},-\frac{A^2}{2B}$

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is ________.

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :

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

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by $y(t)=y_0{\sin }^2\omega t$, where 'y' is measured from the lower end of unstretched spring. Then $\omega$ is:

1. A.$\sqrt{\frac{g}{y_0}}$
2. B.$\frac{1}{2}\sqrt{\frac{g}{y_0}}$
3. C.$\sqrt{\frac{2g}{y_0}}$
4. D.$\sqrt{\frac{g}{2y_0}}$

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

1. A.1.02 eV
2. B.0.81 eV
3. C.0.61 eV
4. D.0.52 eV

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take $g=10m/{\mathrm{s}}^2$. Assume there is no rotational motion and loss of energy after the collision is negligible.]

1. A.23 J
2. B.21 J
3. C.20 J
4. D.19 J

A particle of mass m with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass 3 m at rest. It moves with a velocity $v\hat{j}$ after collision, then, v is given by :

1. A.$v=\sqrt{\frac{2}{3}}u$
2. B.$v=\frac{u}{\sqrt{3}}$
3. C.$v=\frac{u}{\sqrt{2}}$
4. D.$v=\frac{1}{\sqrt{6}}u$

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

A body A of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body B of mass $\frac{m}{2}$ collides with A with a velocity which is half $\left(\frac{\vec{v}}{2}\right)$ the instantaneous velocity $\vec{v}$ of A. The collision is completely inelastic. Then, the combined body :

1. A.starts moving in an elliptical orbit around the planet.
2. B.Falls vertically downwards towards the planet
3. C.Escapes from the Planet's Gravitational field.
4. D.continues to move in a circular orbit

Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$. They collide completely inelastically. The energy lost in the process is :

1. A.$\frac{1}{3}m{u}^2$
2. B.$\frac{1}{8}m{u}^2$
3. C.$\frac{3}{4}m{u}^2$
4. D.$\sqrt{\frac{2}{3}}m{u}^2$

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

A body A, of mass $m=0.1\text{ kg}$ has an initial velocity of $3\hat{i}{\text{ ms}}^{-1}$. It collides elastically with another body, B of the same mass which has an initial velocity of $5\hat{j}{\text{ ms}}^{-1}$. After collision, A moves with a velocity $\vec{v}=4\left(\hat{i}+\hat{j}\right)$. The energy of B after collision is written as $\frac{x}{10}$. The value of x is _______.

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :

1. A.$8.75\times 10^{-3}\text{ J}$
2. B.$1.13\times 10^{-3}\text{ J}$
3. C.$8.75\times 10^{-4}\text{ J}$
4. D.$6.25\times 10^{-4}\text{ J}$

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude ${\theta }_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $\ell (\ell \ll L)$, is close to;

1. A.$mg\ell (1+{\theta }_0^2)$
2. B.$mg\ell$
3. C.$mg\ell \left(1+\frac{{\theta }_0^2}{2}\right)$
4. D.$mg\ell (1-{\theta }_0^2)$

A $25\times 10^{-3}{\mathrm{m}}^3$ volume cylinder is filled with 1 mol of ${\mathrm{O}}_2$ gas at room temperature (300K). The molecular diameter of ${\mathrm{O}}_2$, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an ${\mathrm{O}}_2$ molecule ?

1. A.$\sim 10^{13}$
2. B.$\sim 10^{12}$
3. C.$\sim 10^{11}$
4. D.$\sim 10^{10}$

1. A.6.5 m/s and 3.2 m/s
2. B.6.5 m/s and 6.3 m/s
3. C.3.2 m/s and 6.3 m/s
4. D.3.2 m/s and 12.6 m/s

1. A.$\frac{1}{4\pi {\epsilon }_0}\left[\frac{q^2}{d}+\frac{qQd}{D^2}\right]$
2. B.$\frac{1}{4\pi {\epsilon }_0}\left[-\frac{q^2}{d}-\frac{qQd}{2D^2}\right]$
3. C.$\frac{1}{4\pi {\epsilon }_0}\left[-\frac{q^2}{d}-\frac{qQd}{D^2}\right]$
4. D.$\frac{1}{4\pi {\epsilon }_0}\left[-\frac{q^2}{d}+\frac{2qQd}{D^2}\right]$

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body ?

1. A.1.2 kg
2. B.1.0 kg
3. C.1.8 kg
4. D.1.5 kg

1. A.$1\mathrm{J}$
2. B.$10\mathrm{J}$
3. C.$5\mathrm{J}$
4. D.$30\mathrm{J}$