Laws of Motion — JEE Main PYQs

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the pl …

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^{\circ }$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ( …

A heavy ball of mass M is suspended from the ceiling of car by a light string of mass $\mathrm{m}(\mathrm{m}\ll \mathrm{M})$. When the car is at rest, the speed of transverse waves in the string is 60 ${\mathrm{ms}}^{-1}$. When the car has acceleration a , the wave-speed incre …

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force P , such that the block does not move down …

A ball is thrown upward with an initial velocity ${\mathrm{V}}_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $\mathrm{m}\gamma v^2$ (where m is mass of the ball, $v$ is its Instantneous velocity and $\gamma$ is a constant). Time …

Two masses ${\mathrm{m}}_1=5\mathrm{kg}$ and ${\mathrm{m}}_2=10\mathrm{kg}$, 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 …

Given in the figure are two blocks A and B of weight 20 N and 100 N respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the w …

A block of mass $m$ is placed on a surface with a vertical cross section given by $y=x^3/6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F(t)=F_0{e}^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

Two fixed frictionless inclined plane making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

A block of mass '$m$' is connected to another block of mass '$M$' by a spring (massless) of spring constant '$k$'. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force '$F$' starts acting on the bl …

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ }$ with the initial vertical direction is

A smooth block is released at rest on a $45^{\circ }$ incline and then slides a distance d. The time taken to slide is $n$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to

Consider a car moving on a straight road with a speed of $100\mathrm{m}/\mathrm{s}$. The distance at which car can be stopped is $\left[{\mu }_{\mathrm{k}}=0.5\right]$

Two masses $m_1=5\mathrm{kg}$ and $m_2=4.8\mathrm{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move?
($\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$)

A block rests on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take …

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that