JEE Main Physics — Mechanics previous year questions with solutions.
Distance of the centre of mass of a solid uniform cone from its vertex is ${z}_{0}$. If the radius of its base is $R$ and its height is $h$ then ${z}_{0}$ is equal to:
A particle of mass $2\mathrm{kg}$ is on a smooth horizontal table and moves in a circular path of radius $0.6m$. The height of the table from the ground is $0.8m$. If the angular speed of the particle is $12 \mathrm{rad} {s}^{-1}$ , the magnitude of its angular momentum about a point on the ground right under the center of the circle is:
Two stones are thrown up simultaneously from the edge of a cliff $240m$ high with an initial speed of $10m{s}^{-1}$ and $40m{s}^{-1}$ respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10 {\mathrm{ms}}^{-2}$)(the figure are schematic and not drawn to scale)
A beaker contains a fluid of density $\rho$$\frac{kg}{{m}^{3}}$ , specific heat $S\frac{J}{k{g}^{o}C}$ and viscosity $\eta$ . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $(\frac{\overset{˙}{Q}}{A})$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta$ , $(\frac{S\Delta \theta }{h})$ and $(\frac{1}{\rho g})$ when $\Delta \theta$ ( ${in}^{o}C$ ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(\frac{\overset{˙}{Q}}{A})$ is:
If the capacitance of a nanocapacitor is measured in terms of a unit $u$, made by combining the electronic charge $e$, Bohr radius ${a}_{0}^{},$ Planck's constant $h$ and speed of light $c$ then
A uniform solid cylindrical roller of mass $m$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its centre. If the acceleration of the cylinder is $a$ and it is rolling without slipping then the value of $F$ is:
Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as: <table class="pyq-table"><tbody><tr><td>S.No.</td><td>MS (cm)</td><td>VS divisions</td></tr><tr><td>1.</td><td>0.5</td><td>8</td></tr><tr><td>2.</td><td>0.5</td><td>4</td></tr><tr><td>3.</td><td>0.5</td><td>6</td></tr></tbody></table> If the zero error is - 0.03 cm, then mean corrected diameter is:
From the top of a $64$ metres high tower, a stone is thrown upwards vertically with the velocity of $48 m/s.$ The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g=32 m/{s}^{2}$, is:
A particle is moving in a circle of radius $r$ under the action of a force $F=\alpha {r}^{2}$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy$=0$ for $r=0$):
If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck's constant $h$ are taken as fundamental quantities, the permeability of vacuum ${\mu }_{0}$ can be expressed in units of:
A block of mass $m=10 \mathrm{kg}$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$. When hit by a bullet of mass $50g$ moving with speed $v$, that gets embedded in it, the block moves and comes to stop after moving a distance of $2m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H$, then neglecting energy losses and taking $g=10 m{s}^{-2}$, the value of $H$ is close to
The period of oscillation of a simple pendulum is $T=2\pi \sqrt{\frac{l}{g}}.$ Measured value of $l$ is $20.0\mathrm{cm}$, known to $1\mathrm{mm}$ accuracy and time for $100$oscillations of the pendulum is found to be $90s$ using a wristwatch of $1s$ resolution. The accuracy in the determination of $g$ is
From a solid sphere of mass $M$ and radius $R\text{,}$ a spherical portion of radius $(\frac{R}{2})$ is removed as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty ,$ the potential at the centre of the cavity thus formed is ($G=$gravitational constant) 
A particle is moving in a circular path of radius a, with a constant velocity $\mathrm{v}$ as shown in the figure. The centre of circle is marked by ' $\mathrm{C}$ '. The angular momentum from the origin $\mathrm{O}$ can be written as: 
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is : (density of water is ${\rho }_{\text{w}}$) 
 Two hypothetical planets of masses $\mathrm{m}_1$ and $\mathrm{m}_2$ are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' $d$ '? (Speed of $\mathrm{m}_1$ is $\mathrm{v}_1$ and that of $\mathrm{m}_2$ is $\mathrm{v}_2$ )
From a sphere of mass $M$ and radius $\mathrm{R}$, a smaller sphere of radius $\frac{\mathrm{R}}{2}$ is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is: 
A cylindrical vessel of cross-section A contains water to a height $\mathrm{h}$. There is a hole in the bottom of radius ' $a$ '. The time in which it will be emptied is:
A bullet loses ${(\frac{1}{n})}^{\mathrm{th}}$ of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:
A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :
A spring of unstretched length 1 has a mass $m$ with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is:
Two soap bubbles coalesce to form a single bubble. If $\mathrm{V}$ is the subsequent change in volume of contained air and $\mathrm{S}$ change in total surface area, $\mathrm{T}$ is the surface tension and $\mathrm{P}$ atmospheric pressure, then which of the following relation is correct?
The velocity of water in a river is $18\mathrm{km}{h}^{-1}$ near the surface. If the river is $5m$ deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water$={10}^{-2}\mathrm{poise}$.
A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be :