JEE Main Physics — Mechanics previous year questions with solutions.
A solid sphere of mass $1\mathrm{kg}$ rolls without slipping on a plane surface. Its kinetic energy is $7\times {10}^{-3}J$. The speed of the centre of mass of the sphere is ______ $\mathrm{cm}{s}^{-1}$.
${I}_{\mathrm{CM}}$ is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. ${I}_{\mathrm{AB}}$ is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}R$ from center, where R is the radius of the disc. The ratio of ${I}_{\mathrm{AB}}$ and ${I}_{\mathrm{CM}}$ is $x:9$. The value of $x$ is ______. 
When vector $\vec{A}=2\hat{i}+3\hat{j}+2\hat{k}$ is subtracted from vector $\vec{B}$, it gives a vector equal to $2\hat{j}$. Then the magnitude of vector $\vec{B}$ will be:
Two particles of equal mass $m$ move in a circle of radius $r$ under the action of their mutual gravitational attraction. The speed of each particle will be :
There is an air bubble of radius $1.0\mathrm{mm}$ in a liquid of surface tension $0.075N{m}^{–1}$ and density $1000\mathrm{kg}{m}^{–3}$ at a depth of $10\mathrm{cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ $Pa(g=10m{s}^{-2})$.
Vectors $a\hat{i}+b\hat{j}+\hat{k}$ and $2\hat{i}-3\hat{j}+4\hat{k}$ are perpendicular to each other when $3a+2b=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is _____.
Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the planet also increase. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below
In the arrangement shown in figure ${a}_{1},{a}_{2},{a}_{3}$ and ${a}_{4}$ are the accelerations of masses ${m}_{1},{m}_{2},{m}_{3}$ and ${m}_{4}$ respectively. Which of the following relation is true for this arrangement? 
Two cylindrical vessels of equal cross-sectional area $16{\mathrm{cm}}^{2}$ contain water upto heights $100\mathrm{cm}$ and $150\mathrm{cm}$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water $={10}^{3}\mathrm{kg}{m}^{-3}$ and $g=10{\mathrm{ms}}^{-2}$]
The terminal velocity $({v}_{t})$ of the spherical rain drop depends on the radius $(r)$ of the spherical rain drop as
Two bodies of masses ${m}_{1}=5\mathrm{kg}$ and ${m}_{2}=3\mathrm{kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass ${m}_{1}$ will be : [Take $g=10m{s}^{-2}$] 
A balloon has mass of $10g$ in air. The air escapes from the balloon at a uniform rate with velocity $4.5\mathrm{cm}{s}^{-1}$. If the balloon shrinks in $5s$ completely. Then, the average force acting on that balloon will be (in dyne).
The distance between Sun and Earth is $R$. The duration of year if the distance between Sun and Earth becomes $3R$ will be :
If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :
In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of $0.5s$ is measured from time of $100$ oscillation with a watch of $1s$ resolution. If measured value of length is $10\mathrm{cm}$ known to $1\mathrm{mm}$ accuracy. The accuracy in the determination of $g$ is found to be $x%$. The value of $x$ is
A ball is spun with angular acceleration $\alpha =6{t}^{2}-2t$ where $t$ is in second and $\alpha$ is in $\mathrm{rad}{s}^{-2}$. At $t=0$, the ball has angular velocity of $10\mathrm{rad}{s}^{-1}$ and angular position of $4\mathrm{rad}$. The most appropriate expression for the angular position of the ball is
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R) : Because the angle of contact between the oil/ grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.
Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force ${F}_{1}$ to ${F}_{2}$ is $1:x$ where $x=$_____ . 
A stone of mass $m$, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
Three masses $M=100\mathrm{kg},{m}_{1}=10\mathrm{kg}$ and ${m}_{2}=20\mathrm{kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass ${m}_{2}$ moves upward with an acceleration of $2{\mathrm{ms}}^{-2}$. The value of $F$ is (Take $g=10{\mathrm{ms}}^{-2}$) 
Two balls $A$ and $B$ are placed at the top of $180m$ tall tower. Ball $A$ is released from the top at $t=0s$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t=2s$. After a certain time, both balls meet $100m$ above the ground. Find the value of $u$ in $m{s}^{-1}$. [use $g=10{ms}^{-2}$]
A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws $n$ balls per second, the maximum height the balls can reach is
A particle of mass $500g$ is moving in a straight line with velocity $v=b{x}^{\frac{5}{2}}$. The work done by the net force during its displacement from $x=0$ to $x=4m$ is (Take $b=0.25{m}^{\frac{-3}{2}}{s}^{-1}$).
A screw gauge of pitch $0.5\mathrm{mm}$ is used to measure the diameter of uniform wire of length $6.8\mathrm{cm}$, the main scale reading is $1.5\mathrm{mm}$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is [Screw gauge has $50$ divisions on the circular scale]