JEE Main Physics — Mechanics previous year questions with solutions.
Least count of a vernier caliper is $\frac{1}{20 \mathrm{~N}} \mathrm{~cm}$. The value of one division on the main scale is $1 \mathrm{~mm}$. Then the number of divisions of main scale that coincide with $\mathrm{N}$ divisions of vernier scale is :
A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$) 
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 \mathrm{~mm}$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $1 \mathrm{~mm}$ and it has 100 divisions on circular scale. The diameter of the wire is $\frac{x}{50} \mathrm{~mm}$. The value of $x$ is :
A planet takes $200$ days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?
A bullet is fired into a fixed target looses one third of its velocity after travelling $4\mathrm{cm}$. It penetrates further $D\times {10}^{-3}m$ before coming to rest. The value of $D$ is :
A cricket player catches a ball of mass $120g$ moving with $25m{s}^{-1}$ speed. If the catching process is completed in $0.1s$ then the magnitude of force exerted by the ball on the hand of player will be(in SI unit):
Match List I with List II : 
Four particles, each of mass $1\mathrm{kg}$ are placed at four corners of a square of side $2m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is $______\mathrm{kg}{m}^{2}$.
Three bodies A, B and C have equal kinetic energies and their masses are $400 \mathrm{~g}$. $1.2 \mathrm{~kg}$ and $1.6 \mathrm{~kg}$ respectively. The ratio of their linear momenta is :
A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$
A body of mass $2\mathrm{kg}$ begins to move under the action of a time dependent force given by $\vec{F}=(6t\hat{i}+6{t}^{2}\hat{j})N$. The power developed by the force at the time $t$ is given by:
Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$, the acceleration of the system in $m{s}^{-2}$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) : 
A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$, then the ratio of the masses $\frac{m_2}{m_1}$ is :
A ball of mass $0.5\mathrm{kg}$ is attached to a string of length $50\mathrm{cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400N$. The maximum possible value of angular velocity of the ball in $\mathrm{rad}{s}^{-1}$ is,:
A block of mass $m$ is placed on a surface having vertical cross section given by $y=\frac{{x}^{2}}{4}$. If coefficient of friction is $0.5$, the maximum height above the ground at which block can be placed without slipping is:
A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and density $10^5 \mathrm{~kg} / \mathrm{m}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately: (The coefficient of viscosity of water is $9.8 \times 10^{-6} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2$ )
A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is :
The identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4m$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt{2}}{x}$, where the value of $x$ is ________.
A circular table is rotating with an angular velocity of $\omega \mathrm{rad} / \mathrm{s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $1 \mathrm{~m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \mathrm{~m}$, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is $x \sqrt{2} \omega \mathrm{m} / \mathrm{s}$, where the value of $x$ is _____. 
A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $\mathrm{m}$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :
A disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is: 
A body of weight $200 \mathrm{~N}$ is suspended from a tree branch through a chain of mass $10 \mathrm{~kg}$. The branch pulls the chain by a force equal to (if $g=10 \mathrm{~m} / \mathrm{s}^2$ ) :
Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :
With rise in temperature, the Young's modulus of elasticity