JEE Main Physics — Mechanics previous year questions with solutions.
A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times {10}^{-4}N{\mathrm{cm}}^{-1}$. The radius of drop in $\mathrm{cm}$ will be : (Take : $g=10{\mathrm{ms}}^{-2}$)
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is
The area of cross section of the rope used to lift a load by a crane is $2.5\times {10}^{-4}{m}^{2}$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be (take $g=10{\mathrm{ms}}^{-2}$)
Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be
For $z={a}^{2}{x}^{3}{y}^{\frac{1}{2}}$, where '$a$' is a constant. If percentage error in measurement of '$x$' and '$y$' are $4%$and $12%$, respectively, then the percentage error for '$z$' will be _____$%$.
A batsman hits back a ball of mass $0.4\mathrm{kg}$ straight in the direction of the bowler without changing its initial speed of $15{ms}^{-1}$. The impulse imparted to the ball is _____ $Ns$.
A body of mass $m$ is projected with velocity $\lambda {v}_{e}$ in vertically upward direction from the surface of the earth into space. It is given that ${v}_{e}$ is escape velocity and $\lambda <1$. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ($R$ : radius of earth)
A small spherical ball of radius $0.1\mathrm{mm}$ and density ${10}^{4}\mathrm{kg}{m}^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $h$ will be ____ $m$. (Given $g=10{ms}^{-2}$, viscosity of water $=1.0\times {10}^{-5}N‐s{m}^{-2}$ ).
$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ non-zero constant. Which of the following expression is true for $\vec{A}$?
The Vernier constant of Vernier callipers is $0.1\mathrm{mm}$ and it has zero error of $(-0.05\mathrm{cm})$. While measuring diameter of a sphere, the main scale reading is $1.7\mathrm{cm}$ and coinciding vernier division is $5$ . The corrected diameter will be _____$\times {10}^{-2}\mathrm{cm}$.
An expression of energy density is given by $u=\frac{\alpha }{\beta }\mathrm{sin}(\frac{\alpha x}{kt})$, where $\alpha ,\beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be
In an experiment to determine the Young's modulus, steel wires of five different lengths ($1,2,3,4$ and $5$) but of same cross-section $(2{\mathrm{mm}}^{2})$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x\times {10}^{11}N{m}^{-2}$, then the value of $x$ is _____ . 
A system to $10$ balls each of mass $2\mathrm{kg}$ are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the ${7}^{\mathrm{th}}$ and ${8}^{\mathrm{th}}$ ball is _____ $N$ when ${6}^{\mathrm{th}}$ ball just leaves the table. 
Two satellites $A$ and $B$ having masses in the ratio $4:3$ are revolving in circular orbits of radii $3r$ and $4r$ respectively around the earth. The ratio of total mechanical energy of $A$ to $B$ is
A block of mass $M$ placed inside a box descends vertically with acceleration $a$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of $'a'$ will be
Two blocks of masses $10\mathrm{kg}$ and $30\mathrm{kg}$ are placed on the same straight line with coordinates $(0,0)\mathrm{cm}$ and $(x,0)\mathrm{cm}$ respectively. The block of $10\mathrm{kg}$ is moved on the same line through a distance of $6\mathrm{cm}$ towards the other block. The distance through which the block of $30\mathrm{kg}$ must be moved to keep the position of centre of mass of the system unchanged is
A pressure-pump has a horizontal tube of cross-sectional area $10{\mathrm{cm}}^{2}$ for the outflow of water at a speed of $20m{s}^{-1}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water $=1000\mathrm{kg}{m}^{-3}$]
Consider a cylindrical tank of radius $1m$ is filled with water. The top surface of water is at $15m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5m$ from the bottom. A force of $5\times {10}^{5}N$ is applied an the top surface of water using a piston. The speed of efflux from the hole will be : (given atmospheric pressure ${P}_{A}=1.01\times {10}^{5}Pa$, density of water ${\rho }_{w}=1000\mathrm{kg}{m}^{-3}$ and gravitational acceleration $g=10m{s}^{-2}$) 
The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times {10}^{-4}$ is _____ $\mathrm{kJ}{m}^{-3}$. Assume that material is elastic upto the linear strain of $5\times {10}^{-4}$, 
From the top of a tower, a ball is thrown vertically upward which reaches the ground in $6s$. A second ball thrown vertically downward from the same position with the same speed reaches the ground in $1.5s$. A third ball released, from the rest from the same location, will reach the ground in _____ s.
A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if :
The velocity of a small ball of mass $m$ and density ${d}_{1}$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is ${d}_{2}$, then the viscous force acting on the ball, will be
In a vernier callipers, each $\mathrm{cm}$ on the main scale is divided into $20$ equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _____ $\times {10}^{-2}\mathrm{mm}$
Identify the pair of physical quantities that have same dimensions: