JEE Main Physics — Mechanics previous year questions with solutions.
Potential energy as a function of $r$ is given by $U=\frac{A}{{r}^{10}}-\frac{B}{{r}^{5}}$, where $r$ is the interatomic distance, $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be :
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $5$ times its mass? (Assume the collision to be head-on elastic collision)
A torque meter is calibrated to reference standards of mass, length and time each with $5%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of
A block of mass $200g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F=\sqrt{x}N$ as shown in figure.  The value of $x=_____$.
A monkey of mass $50\mathrm{kg}$ climbs on a rope which can withstand the tension $(T)$ of $350N$. If monkey initially climbs down with an acceleration of $4m{s}^{-2}$ and then climbs up with an acceleration of $5m{s}^{-2}$. Choose the correct option $(g=10m{s}^{-2})$
If force $\vec{F}=3\hat{i}+4\hat{j}-2\hat{k}$ acts on a particle having position vector $2\hat{i}+\hat{j}+2\hat{k}$ then, the torque about the origin will be:
A pulley of radius $1.5m$ is rotated about its axis by a force $F=(12t-3{t}^{2})N$ applied tangentially (while $t$ is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $4.5\mathrm{kg}{m}^{2}$, the number of rotations made by the pulley before its direction of motion is reversed, will be $\frac{K}{\pi }$. The value of $K$ is _____ .
Three identical particle $A,B$ and $C$ of mass $100\mathrm{kg}$ each are placed in a straight line with $AB=BC=13m$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13m$ from the particle $B$ on the perpendicular bisector of the line $AC$. The value of $F$ will be approximately
A solid cylinder and a solid sphere, having same mass $M$ and radius $R$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be
A NCC parade is going at a uniform speed of $9\mathrm{km}{h}^{-1}$ under a mango tree on which a monkey is sitting at a height of $19.6m$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given $g=9.8m{s}^{-2}$)
Water falls from a $40m$ high dam at the rate of $9\times {10}^{4}\mathrm{kg}$ per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of $100W$ lamps, that can be lit, is (Take $g=10{\mathrm{ms}}^{-2}$)
If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be
The elongation of a wire on the surface of the earth is ${10}^{-4}m$. The same wire of same dimensions is elongated by $6\times {10}^{-5}m$ on another planet. The acceleration due to gravity on the planet will be _____ $m{s}^{-2}$. (Take acceleration due to gravity on the surface of earth $=10{ms}^{-2}$)
Which of the following relations is true for two unit vector $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each other?
A spherical shell of $1\mathrm{kg}$ mass and radius $R$ is rolling with angular speed $\omega$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin $O$ is $\frac{a}{3}{R}^{2}\omega$. The value of $a$ will be 
A ball of mass $100g$ is dropped from a height $h=10\mathrm{cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is _____ $N{m}^{-1}$ (Use $g=10{ms}^{-2}$) 
A uniform chain of $6m$ length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is $0.5$, the maximum length of the chain hanging from the table is _____ $m$.
If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be
A torque meter is calibrated to reference standards of mass, length and time each with $5%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1%,2%$ and $3%$ respectively. The maximum percentage error in the detection of the dissipated heat will be:
A steel wire of length $3.2m({Y}_{S}=2.0\times {10}^{11}N{m}^{-2})$ and a copper wire of length $4.4m({Y}_{C}=1.1\times {10}^{11}N{m}^{-2})$ , both of radius $1.4\mathrm{mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\mathrm{mm}$. The load applied, in Newton, will be: (Given $\pi =\frac{22}{7}$)
In an experiment of determine the Young's modulus of wire of a length exactly $1m$, the extension in the length of the wire is measured as $0.4\mathrm{mm}$ with an uncertainty of $\pm 0.02\mathrm{mm}$ when a load of $1\mathrm{kg}$ is applied. The diameter of the wire is measured as $0.4\mathrm{mm}$ with an uncertainty of $\pm 0.01\mathrm{mm}$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x\times {10}^{10}N{m}^{-2}$. The value of $x$ is _____ .
A silver wire has a mass $(0.6\pm 0.006)g$, radius $(0.5\pm 0.005)\mathrm{mm}$ and length $(4\pm 0.04)\mathrm{cm}$. The maximum percentage error in the measurement of its density will be
A silver wire has a mass $(0.6\pm 0.006)g$, radius $(0.5\pm 0.005)\mathrm{mm}$ and length $(4\pm 0.04)\mathrm{cm}$. The maximum percentage error in the measurement of its density will be