JEE Main Physics — Mechanics previous year questions with solutions.
A body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$ . And the other mass, in a circular orbit of radius $\frac{3R}{2}.$ The difference between the final and the initial total energies is
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 
The mass of a hydrogen molecule is $3.32\times {10}^{-27 }\mathrm{kg}.$ If ${10}^{23}$ hydrogen molecules strike, per second, a fixed wall of the area $2 {\mathrm{cm}}^{2}$ at an angle of ${45}^{o}$ to the normal, and rebound elastically with a speed of ${10}^{3}m{s}^{-1},$ then the pressure on the wall is nearly:
Let $\vec{A}=(\hat{i} + \hat{j}) and \vec{B}=(2\hat{i}- \hat{j})$ . The magnitude of a coplanar vector $\vec{C}$ such that $\vec{A} . \vec{C}=\vec{B}. \vec{C}= \vec{A} . \vec{B}$ is given by:
Take the mean distance of the moon and the sun from the earth to be $0.4 \times 10^6 \mathrm{~km}$ and $150 \times 10^6 \mathrm{~km}$ respectively. Their masses are $8 \times 10^{22} \mathrm{~kg}$ and $2 \times$ $10^{30} \mathrm{~kg}$ respectively. The radius of the earth is $6400 \mathrm{~km}$. Let $\Delta F_1$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta \mathrm{F}_2$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta F_1}{\Delta F_2}$ is:
A proton of mass $\mathrm{m}$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^{\circ}$ with respect to each other. The mass of unknown particle is:
A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let ${P}_{2}$ be the pressure inside the inner bubble and ${P}_{0}$, the pressure outside the outer bubble. Radius of another bubble with pressure difference ${P}_{2}-{P}_{0}$ between its inside and outside would be:
Take the mean distance of the moon and the sun from the earth to be $0.4\times {10}^{6}\mathrm{km}$ and $150\times {10}^{6}\mathrm{km}$, respectively. Their masses are $8\times {10}^{22}$ $\mathrm{kg}$ and $2\times {10}^{30}$ $\mathrm{kg}$, respectively. The radius of the earth is $6400\mathrm{km}$. Let $\Delta {F}_{1}$ be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and $\Delta {F}_{2}$ be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta {F}_{1}}{\Delta {F}_{2}}$ is,
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area $a$ floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $(\frac{dr}{r})$ , is:
When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{5 \mathrm{r}}{4}$. Taking the atmospheric pressure to be equal to $10 \mathrm{~m}$ height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):
The relative error in the determination of the surface area of a sphere is $\alpha$. The relative error in the determination of its volume is
A conical pendulum of length $l$ makes an angle $\theta =45^{\circ}$ with respect to $Z-$axis and moves in a circle in the $XY$ plane. The radius of the circle is $0.4m$ and its center is vertically below $O$. The speed of the pendulum, in its circular path, will be - $(Take g=10 m{s}^{-2})$ 
An object is dropped from a height $h$ from the ground. Every time it hits the ground it loses $50%$ of its kinetic energy. The total distance covered as $t\rightarrow \infty$ is:
A uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. A string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is: 
Two tubes of radii ${r}_{1}$ and ${r}_{2}$ and lengths ${l}_{1}$ and ${l}_{2,}$ respectively, are connected in series and a liquid flows through each of them in stream line conditions. ${P}_{1}$ and ${P}_{2}$ are pressure differences across the two tubes. If ${P}_{2}$ is $4{P}_{1}$ and ${l}_{2}$ is $\frac{ {l}_{1} }{ 4 }$ then the radius ${r}_{2}$ will be equal to :
A physical quantity $P$ is described by the relation $P={a}^{\frac{1}{2}} {b}^{2} {c}^{3}{d}^{-4}$. If the relative errors in the measurement of $a$, $b$, $c$ and $d$ respectively, are $2%$, $1%$, $3%$ and $5%$. Then the relative error in $P$ will be:
Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:
Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in figure. They collide completely inelastic and move as a single particle $C$. The angle $\theta$ that the path of $C$ makes with the $X$-axis is given by- 
Moment of inertia of an equilateral triangular lamina $ABC$, about the axis passing through its centre $O$ and perpendicular to its plane is ${I}_{0}$ as shown in the figure. A cavity $DEF$ is cut out from the lamina, where $D,E,F$ are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is: 
In a physical balance working on the principle of moments, when $5 \mathrm{mg}$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
A slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is: 
Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?
A circular hole of radius $\frac{R}{4}$ is made in a thin uniform disc having mass and radius $R$, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point $O$ and perpendicular to the plane of the disc is- 