JEE Main Physics — Mechanics previous year questions with solutions.
A thin uniform rod $(X)$ of mass $M$ and length $L$ is pivoted at a height $\left(\frac{L}{3}\right)$ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is $\_\_\_\_$. ($\mathrm{g}=$ gravitational acceleration) 
A spherical ball of mass $2$ kg falls from a height of $10$ m and is brought to rest after penetrating $10$ cm into sand. The average force exerted by sand on the ball is _______ N. (Take $g = 10$ m/s$^2$)
Given below are two statements : Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles. Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference. In the light of the above statements, choose the correct answer from the options given below :
Surface tension of two liquids (having same densities), $T_{1}$ and $T_{2}$, are measured using capillary rise method utilizing two tubes with inner radii of $r_{1}$ and $r_{2}$ where $r_{1}>r_{2}$. The measured liquid heights in these tubes are $h_{1}$ and $h_{2}$ respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights $h_{1}$ and $h_{2}$ and surfaces tensions $T_{1}$ and $T_{2}$ satisfy the relation:
In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text{th}}$ Vernier division coincides with a main scale reading. If the value of $1$ main scale division is $1$ mm and there are $10$ Vernier scale divisions, then the Vernier caliper has
The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20 \mathrm{~cm} / \mathrm{s}$. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be $\_\_\_\_$ $\mathrm{cm} / \mathrm{s}$.
Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8$ N/m$^2$. Area of cross-section of upper wire is $0.008$ cm$^2$ and of lower wire is $0.004$ cm$^2$. The maximum mass that can be added to pan without breaking any wire is _____ kg. (take $g = 10$ m/s$^2$) 
Given below are two statements: Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. Statement II: The time period of revolution of the satellite is $T=2 \pi \sqrt{\frac{R_{e}}{g}}$ (for satellite very close to the earth surface), where $R_{\mathrm{e}}$ radius of earth and $g$ acceleration due to gravity. In the light of the above statements, choose the correct answer from the options given below :
From $18$ m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is _____ m. (Take $g = 10$ m/s$^2$ and neglect the air resistance)
A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional errors of $0.1,0.2$ and 0.5 , respectively in measurement. The maximum fractional error of Q is
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At $t=5 \mathrm{~s}$, maximum percentage error in the energy is :
A bead of mass ' $m$ ' slides without friction on the wall of a vertical circular hoop of radius ' $R$ ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' $R$ '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity) 
A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are 
Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.
Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is $\ldots\ldots$ g.
A person travelling on a straight line moves with a uniform velocity $\mathrm{v}_1$ for a distance x and with a uniform velocity $\mathrm{v}_2$ for the next $\frac{3}{2} \mathrm{x}$ distance. The average velocity in this motion is $\frac{50}{7} \mathrm{~m} / \mathrm{s}$. If $\mathrm{v}_1$ is $5 \mathrm{~m} / \mathrm{s}$ then $\mathrm{v}_2=$ _________ $\mathrm{m} / \mathrm{s}$.
The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km . 
A ball of mass 100 g is projected with velocity $20 \mathrm{~m} / \mathrm{s}$ at $60^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is
 A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{~rad} / \mathrm{s}^2$. Moment of inertia of the wheel is _____ $\mathrm{kg} \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$)
A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is 
If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is
Match List - I with List - II. 
If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.
A helicopter flying horizontally with a speed of $360 \mathrm{~km} / \mathrm{h}$ at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is : (use acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and neglect air resistance)