JEE Main Physics — Mechanics previous year questions with solutions.
Electric field in a certain region is given by $\vec{E}=(\frac{A}{{x}^{2}}\hat{i}+\frac{B}{{y}^{3}}\hat{j})$. The SI unit of $A$ and $B$ are :
The frequency $(\nu )$ of an oscillating liquid drop may depend upon radius $(r)$ of the drop, density $(\rho )$ of liquid and the surface tension $(s)$ of the liquid as: $\nu ={r}^{a}{\rho }^{b}{s}^{c}$. The values of $a,b$ and $c$ respectively are
Two trains $A$ and $B$ of length $l$ and $4l$ are travelling into a tunnel of length $L$ in parallel tracks from opposite directions with velocities $108\mathrm{km}{h}^{-1}$ and $72\mathrm{km}{h}^{-1},$ respectively. If train $A$ take $35s$ less time than train $B$ to cross the tunnel then, length $L$ of tunnel is: (Given $L=60l$)
A passenger sitting in a train A moving at $90\mathrm{km}{h}^{-1}$ observes another train B moving in the opposite direction for $8s$. If the velocity of the train B is $54\mathrm{km}{h}^{-1}$, then length of train B is:
A person travels $x$ distance with velocity ${v}_{1}$ and then $x$ distance with velocity ${v}_{2}$ in the same direction. The average velocity of the person is $v$, then the relation between $v,{v}_{1}$ and ${v}_{2}$ will be
A vehicle travels $4\mathrm{km}$ with speed of $3\mathrm{km}{h}^{-1}$ and another $4\mathrm{km}$ with speed of $5\mathrm{km}{h}^{-1}$, then its average speed is :
A car travels a distance of $x$ with speed ${v}_{1}$ and then same distance $x$ with speed ${v}_{2}$ in the same direction. The average speed of the car is:
A disc is rolling without slipping on a surface. The radius of the disc is $R.$ At $t=0,$ the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is 
A projectile fired at $30^{\circ}$ to the ground is observed to be at same height at time $3s$ and $5s$ after projection, during its flight. The speed of projection of the projectile is $m{s}^{-1}$. (Given $g=10m{s}^{-2}$)
Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ},$ the ratio of instantaneous velocity to its average velocity is $\pi :x\sqrt{2}.$ The value of $x$ will be
A child stands on the edge of the cliff $10m$ above the ground and throws a stone horizontally with an initial speed of $5m{s}^{–1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be _____ $m{s}^{–1}$ (given, $g=10m{s}^{–2}$ ).
An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $x=+2m$, its velocity is $-4\hat{j}m{s}^{-1}$ . The object’s velocity $(v)$ and acceleration $(a)$ at $x=–2m$ will be
A body of mass $500g$ moves along $x$-axis such that it's velocity varies with displacement $x$ according to the relation $v=10\sqrt{x}m{s}^{-1}$ the force acting on the body is:
A coin placed on a rotating table just slips when it is placed at a distance of $1\mathrm{cm}$ from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre:
A block of mass $5\mathrm{kg}$ is placed at rest on a table of rough surface. Now, if a force of $30N$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50m$ in an interval of time $10s$. Coefficient of kinetic friction is (given, $g=10m{s}^{–2}$ ):
Consider a block kept on an inclined plane (inclined at $45^{\circ}$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane $(\mu )$ is equal to : .
In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as $5.25\mathrm{mm}$ and apparent thickness of the glass slab at $5.00\mathrm{mm}$. Travelling microscope has $20$ divisions in one $\mathrm{cm}$ on main scale and $50$ divisions on Vernier scale is equal to $49$ divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $\frac{x}{10}\times {10}^{-3}$, where $x$ is ______
The speed of a swimmer is $4\mathrm{km}{h}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $1\mathrm{km}$, he reaches a point $750m$ down the stream on the opposite bank. The speed of the river water is ______ $\mathrm{km}{h}^{-1}$.
A thin uniform rod of length $2m$, cross sectional area $A$ and density $d$ is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{Ad}}$, then the value of $\alpha$ is ______.
Two projectiles $A$ and $B$ are thrown with initial velocities of $40m{s}^{-1}$ and $60m{s}^{-1}$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $(g=10m{s}^{-2})$
As shown in figure, a $70\mathrm{kg}$ garden roller is pushed with a force of $\vec{F}=200N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10m{s}^{-2}$) 
A stone tied to $180\mathrm{cm}$ long string at its end is making $28$ revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x}m{s}^{-2}$. The value of $x$ ______. [Take $\pi =\frac{22}{7}$]
The distance travelled by an object in time $t$ is given by $s=(2.5){t}^{2}$ . The instantaneous speed of the object at$t=5s$ will be :