JEE Main Physics — Mechanics previous year questions with solutions.
A body travels $102.5 \mathrm{~m}$ in $\mathrm{n}^{\text {th }}$ second and $115.0 \mathrm{~m}$ in $(\mathrm{n}+2)^{\text {th }}$ second. The acceleration is :
A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$. Its acceleration at any time $\mathrm{t}$ is $x^{-\mathrm{n}}$ where $\mathrm{n}=$ ___________
Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $\mathrm{AB}$ as shown in figure is $\sqrt{8 / x}$. The value of $x$ is : 
To find the spring constant $(k)$ of a spring experimentally, a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in measurement of mass. The percentage error in determining value of $k$ is :
Given below are two statements: Statement (I) : Planck's constant and angular momentum have the same dimensions. Statement (II) : Linear momentum and moment of force have the same dimensions. In light of the above statements, choose the correct answer from the options given below :
The co-ordinates of a particle moving in $x-y$ plane are given by : $x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$. The motion of the particle is :
A particle starts from origin at $t=0$ with a velocity $5\hat{i}m{s}^{-1}$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j})m{s}^{-2}$. If the $x$-coordinate of the particle at that instant is $84m$, then the speed of the particle at this time is $\sqrt{\alpha }m{s}^{-1}$. The value of $\alpha$ is _______.
Two forces $\bar{F}_1$ and $\bar{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\vec{F}_2$ is $\cos ^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is _____.
Match List-I with List-II : $\begin{array}{|c|c|c|c|} \hline & \text { List-I } & & \text { List-II } \\ \hline \text { (A) } & \text { A force that restores an elastic body of unit area to its original state } & \text { (I) } & \text { Bulk modulus } \\ \hline \text { (B) } & \text { Two equal and opposite forces parallel to opposite faces } & \text { (II) } & \text { Young's modulus } \\ \hline \text { (C) } & \begin{array}{l} \text { Forces perpendicular everywhere to the surface per unit area } \\ \text { same everywhere } \end{array} & \text { (III) } & \text { Stress } \\ \hline \text { (D) } & \text { Two equal and opposite forces perpendicular to opposite faces } & \text { (IV) } & \text { Shear modulus } \\ \hline \end{array}$ Choose the correct answer from the options given below :
A body of mass $4\mathrm{kg}$ experiences two forces ${\vec{F}}_{1}=5\hat{i}+8\hat{j}+7\hat{k}$ and ${\vec{F}}_{2}=3\hat{i}-4\hat{j}-3\hat{k.}$ The acceleration acting on the body is:
A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is _____ .
A particle initially at rest starts moving from reference point $x=0$ along $x$-axis, with velocity $v$ that varies as $v=4\sqrt{x}m{s}^{-1}$. The acceleration of the particle is _____ $m{s}^{-2}$.
An artillery piece of mass ${M}_{1}$ fires a shell of mass ${M}_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :
A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2>m_1$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:
A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text {th }}$ division on the main scale. The least count of the instrument is $0.1 \mathrm{~mm}$. One main scale division is equal to _____$\mathrm{mm}$.
A player caught a cricket ball of mass $150 \mathrm{~g}$ moving at a speed of $20 \mathrm{~m} / \mathrm{s}$. If the catching process is completed in $0.1 \mathrm{~s}$, the magnitude of force exerted by the ball on the hand of the player is:
The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1 \mathrm{~mm}$. The main scale reading is $2 \mathrm{~cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:
A heavy iron bar of weight $12\mathrm{kg}$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ}$ with the horizontal, the normal force applied by the man on bar is:
The maximum height reached by a projectile is $64 \mathrm{~m}$. If the initial velocity is halved, the new maximum height of the projectile is _____ $\mathrm{m}$.
A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of $\mathrm{A}$ is _______ $\times 10^{-4} \mathrm{~m}^2$ (consider $x< < \mathrm{L}$ ). (given : $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
The gravitational potential at a point above the surface of earth is $-5.12\times {10}^{7}J{\mathrm{kg}}^{-1}$ and the acceleration due to gravity at that point is $6.4m{s}^{-2}$. Assume that the mean radius of earth to be $6400\mathrm{km}$. The height of this point above the earth's surface is:
A uniform rod $AB$ of mass $2\mathrm{kg}$ and Length $30\mathrm{cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2Ns$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi }{x}s,$ where $x=$ ____.
Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?
A body starts moving from rest with constant acceleration covers displacement ${S}_{1}$ in first $(p-1)$ seconds and ${S}_{2}$ in first $p$ seconds. The displacement ${S}_{1}+{S}_{2}$ will be made in time :