JEE Main Physics — Mechanics previous year questions with solutions.
A bottle has an opening of radius $a$ and length $b$. A cork of length $b$ and radius $(a+\Delta a)$ where $(\Delta a\ll a)$, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is $B$ and the coefficient of friction between the bottle and cork is $\mu$, then the force needed to push the cork into the bottle is 
An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$, while its mass is $M$. The gravitational pull ${F}_{G}$ on the astronaut is
A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction ${\mu }_{min}$ between the mass and the inclined surface such that the mass does not move is:
A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 m{s}^{-1}$ , the car needs power P. If it needs power $\frac{P}{2}$ while moving downhill at speed $\upsilon$ then value of $\upsilon$ is:
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to : (Take the radius of the drum to be 1.25 m and its axle to be horizontal) :
The figure shows an elliptical path $ABCD$ of a planet around the sun $S$ such that the area of triangle $CSA$ is $\frac{1}{4}$ the area of the ellipse. (see figure) with $DB$ as the major axis, and $CA$ as the minor axis. If ${t}_{1}$ is the time taken for the planet to go over path $ABC$ and ${t}_{2}$ for path taken over $CDA$ then: 
A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by ${n}^{2}R{t}^{2}$, where $n$ is a constant. The power delivered to the particle by the force acting on it, is :
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:
A screw gauge with a pitch of $0.5 \mathrm{mm}$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the ${45}^{th}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5\mathrm{mm}$ and the ${25}^{th}$ division coincides with the main scale line?
 Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r $(r<<R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then:
A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L$. The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R$, respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal:
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to ${T}_{M}$ . If the Young's modulus of the material of the wire is $Y$, then $\frac{1}{Y}$ is equal to: ($g=$gravitational acceleration)
A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$, then
 Given in the figure are two blocks $A$ and $B$ of weight $20N$ and $100N$, respectively. These are being pressed against a wall by a force $F$ and kept in equilibrium as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall on block $B$ is:
Which of the following most closely depicts the correct variation of the gravitation potential, $V(r)$ with distance $r$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)
From a solid sphere of mass $M$ and radius $R$, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:
A block of mass $m=0.1 \mathrm{kg}$ is connected to a spring of unknown spring constant k. It is compressed to a distance $x$ from its equilibrium position and released from rest. After approaching half the distance $(\frac{x}{2})$ from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity $3 m{s}^{-1}$. The total initial energy of the spring is:
A uniform thin rod AB of length $L$ has linear mass density $\mu (x)=a+\frac{bx}{L}$, where $x$ is measured from A. If the CM of the rod lies at a distance of $(\frac{7}{12}L)$ from A, then $a$ and $b$ are related as:
A vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radians $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$ . In that case $|\vec{B}-\vec{A}|$ is :
If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: 
Consider a thin uniform square sheet made of a rigid material. If its side is $a$, mass m and moment of inertia $I$ about one of its diagonals, then:
A particle of mass $\text{m}$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:
If a body moving in a circular path maintains constant speed of $10 m{s}^{-1}$ , then which of the following correctly describes the relation between acceleration and radius?
A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L(L\gg r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed $v$, the average force experienced by each support after a long time is (assume all collisions are elastic): 