JEE Main Physics — Mechanics previous year questions with solutions.
The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is
A uniform rod $AB$ is suspended from a point $X$, at a variable distance $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m,x)$ value is recorded. The appropriate variables that give a straight line, when plotted, are: 
An automobile, travelling at $40 \mathrm{~km} / \mathrm{h}$, can be stopped at a distance of $40 \mathrm{~m}$ by applying brakes. If the same automobile is travelling at $80 \mathrm{~km} / \mathrm{h}$, the minimum stopping distance, in metres, is (assume no skidding)
The percentage errors in quantities $P$, $Q$, $R$ and $S$ are $0.5%$, $1%$, $3%$ and $1.5%$ respectively in the measurement of a physical quantity $A= \frac{ {P}^{3} {Q}^{2} }{ \sqrt{ R } S }$. The maximum percentage error in the value of $A$ will be:
A disc rotates about its axis of symmetry in a hoizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distance of $1.25 \mathrm{~cm}$ from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$
A body of mass $2 \mathrm{~kg}$ slides down with an acceleration of $3 \mathrm{~m} / \mathrm{s}^2$ on a rough inclined plane having a slope of $30^{\circ}$. The external force required to take the same body up the plane with the same acceleration will be: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$
A body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$, and the other mass, in a circular orbit of radius $\frac{3 R}{2}$. The difference between the final and initial total energies is:
A force of $40 \mathrm{~N}$ acts on a point $\mathrm{B}$ at the end of an L-shaped object, as shown in the figure. The angle $\theta$ that will produce maximum moment of the force about point $\mathrm{A}$ is given by: 
An automobile, traveling at $40\mathrm{km}{h}^{-1}$, can be stopped at a distance of $40m$ by applying brakes. If the same automobile is traveling at $80\mathrm{km}{h}^{-1}$, the minimum stopping distance in metres is (Assume no skidding):
It is found that if a neutron suffers an elastic collinear collision with a deuterium at rest, the fractional loss of its energy is ${P}_{d}$, while for its similar collision with a carbon nucleus at rest, the fractional loss of energy is ${P}_{c}$. The values of ${P}_{d}$ and ${P}_{c}$ are respectively
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of $0.25$ $\mathrm{cm}$. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is:
A thin rod $\mathrm{MN}$, free to rotate in the vertical plane about the fixed end $\mathrm{N}$, is held horizontal. When the end $\mathrm{M}$ is released the speed of this end, when the rod makes an angle $\alpha$ with the horizontal, will be proportional to: (see figure) 
A given object takes $n$ times more time to slide down a ${45}^{o}$ rough inclined plane as it takes to slide down a perfectly smooth ${45}^{o}$ incline. The coefficient of kinetic friction between the object and the incline is:
A given object takes $n$ times more time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is :
From a uniform circular disc of radius R and mass 9 M, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is: 
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $\mathrm{G}, \mathrm{h}$ and $\mathrm{c}$. Which of the following correctly gives the Planck length?
A body of mass $m$ starts moving from rest along $x-$axis so that its velocity varies as $v=a\sqrt{s}$ where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first $t$ second after the start of the motion is
The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively. 
A force of $40N$ acts on a point $B$ at the end of an L-shaped object as shown in the figure. The angle $\theta$ that will produce the maximum moment of the force about point $A$ is given by: 
In a collinear collision, a particle with an initial speed ${v}_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is
A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ${\rho }_{1}$ and ${\rho }_{2} ({\rho }_{1}>{\rho }_{2} ),$ fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical is:
A thin uniform bar of length $\mathrm{L}$ and mass $8 \mathrm{~m}$ lies on a smooth horizontal table. Two point masses $\mathrm{m}$ and $2 \mathrm{~m}$ moving in the same horizontal plane from opposite sides of the bar with speeds $2 \mathrm{v}$ and $v$ respectively. The masses stick to the bar after collision at a distance $\frac{\mathrm{L}}{3}$ and $\frac{\mathrm{L}}{6}$ respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be: 
Two masses ${m}_{1}=5 \mathrm{kg}$ and ${m}_{2}=10 \mathrm{kg}$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is $0.15$. The minimum weight m that should be put on top of ${m}_{2}$ to stop the motion is: 
A thin uniform tube is bent into a circle of radius $r$ in the virtical plane. Equal volumes of two immiscible liquids, whose densities are $\rho_1$ and $\rho_2\left(\rho_1>\rho_2\right)$ fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical is