JEE Main Physics — Mechanics previous year questions with solutions.
If a body of mass $1$ kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $v$ and $k$ respectively are _______. (Take radius of earth to be $6400$ km and $g = 9.8$ m/s$^2$)
A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M/8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2R$. If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2/I_1 = $ _____.
A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is $6.4$ m. The speed of the bullets from the gun is ______ m/s. (take $g=10$ m/s$^2$)
An object is projected with kinetic energy $K$ from a point $A$ at an angle $60^{\circ}$ with the horizontal. The ratio of the difference in kinetic energies at points $B$ and $C$ to that at point $A$ (see figure), in the absence of air friction is : 
Given below are two statements : Statement I: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int_{r_{1}}^{r_{2}} \vec{F} \cdot \overrightarrow{d r}$. Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :
Figure represents the extension ($\Delta l$) of a wire of length $1$ meter, suspended from the ceiling of the room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5}$ m$^2$ then the Young's modulus of the wire is __________ N/m$^2$. 
Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is $\_\_\_\_$ m. $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Two blocks ($P$ and $Q$) with respectively masses $2$ kg and $1.5$ kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube ($S$), as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube ($S$) moves towards the right with acceleration of $\dfrac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is _______. (take $g = 10$ m/s$^2$) 
A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $20 \mathrm{~m} / \mathrm{s}$ when its direction of motion is $45^{\circ}$ with the horizontal. The initial speed of the projectile is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.
Two identical thin rods of mass $M \mathrm{~kg}$ and length $L \mathrm{~m}$ are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point $P$ and perpendicular to the plane of the rods is $\frac{x}{12} \mathrm{ML}^{2} \mathrm{~kg} \mathrm{~m}^{2}$. The value of $x$ is $\_\_\_\_$. 
A uniform rod of mass $m$ and length $l$ suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is $\_\_\_\_$. $(g$ acceleration due to gravity) 
Three masses $200 \mathrm{~kg}, 300 \mathrm{~kg}$ and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process $\_\_\_\_$ J. (Gravitational constant $\mathrm{G}=6.7 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}$)
The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m$, $l$ and $d$ are $97.42 \pm 0.02$ g, $8.35 \pm 0.05$ mm and $20.20 \pm 0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ is _______.
A small block of mass $m$ slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_{0}$. The angle between the inclined plane and ground is $\theta$ and its base length is $L$. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is $\_\_\_\_$. 
A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is $\_\_\_\_$. ($g=$ gravitational acceleration)
A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h = \alpha R$. The value of $\alpha$ is _______. 
A copper wire of length $3\text{ m}$ is stretched by $3\text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6}\text{ m}^3$. The elastic potential energy stored in the wire in stretched condition would be _______ J. (Given Young modulus of copper $= 1.1 \times 10^{11}\text{ N/m}^2$)
A lift of mass $1600$ kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^8$ N/m$^2$ and its radius is $4$ mm, then maximum acceleration the lift can take is _______ m/s$^2$. (take $g = 10$ m/s$^2$ and $\pi = 3.14$)
A metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. Second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross sections of strings $A$ and $B$ are same. The ratio of lengths of strings of $A$ to $B$ is $2$ and the ratio of their Young's moduli $(Y_A/Y_B)$ is $0.5$. The ratio of elongations in $A$ to $B$ is ______.
Two wires $A$ and $B$ made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections $3.0 \times 10^{-5} \mathrm{~m}^{2}$ and $4.5 \times 10^{-5} \mathrm{~m}^{2}$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x: 3$. The value of $x$ is $\_\_\_\_$.
Match the LIST-I with LIST-II \(\begin{array}{||c|l||c||l||} \hline & \textbf{List-I} & & \textbf{List-II} \\ \hline A. & \text{Spring constant} & I. & \mathrm{M L^{2} T^{-2} K^{-1}} \\ \hline B. & \text{Thermal conductivity} & II. & \mathrm{M L^{0} T^{-2}} \\ \hline C. & \text{Boltzmann constant} & III. & \mathrm{M L^{2} T^{-3} A^{-2}} \\ \hline D. & \text{Inductive reactance} & IV. & \mathrm{M L T^{-3} K^{-1}} \\ \hline \end{array}\) Choose the correct answer from the options given below:
A cylindrical vessel of $40$ cm radius is completely filled with water and its capacity is $528$ dm$^3$ (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at $70$ cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm.
The surface tension of a soap bubble is $0.03$ N/m. The work done in increasing the diameter of bubble from $2$ cm to $6$ cm is $\alpha \pi \times 10^{-4}$ J. The value of $\alpha$ is _______. (Take $\pi = 3.14$)
A small metallic sphere of diameter 2 mm and density $10.5 \mathrm{~g} / \mathrm{cm}^{3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5 \mathrm{~g} / \mathrm{cm}^{3}$ respectively. The terminal velocity attained by the sphere is $\_\_\_\_$ $\mathrm{cm} / \mathrm{s}$. ($\pi=\frac{22}{7}$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$)