A system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley P. The mass $m_3$ hangs freely and $m_1$ and $m_2$ are on a rough horizontal table (the coefficient of friction $\mu).$ The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_3$ is (Assume $m_1 = m_2 = m_3 = m$)

The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph. The change in momentum of the particle over the time interval from zero to 8 s is

A solid cylinder of mass $50$ kg and radius $0.5$ m is free to rotate about a horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other hanging freely. The tension in the string required to produce an angular acceleration of $2$ rev/s$^2$ is

A block A of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end another block B of mass $m_2$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu_k.$ When the block A is sliding on the table, the tension in the string is

Three blocks A, B and C of masses 4, 2 and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied onto the 4 kg block, then the contact force between A and B is

A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is

Two blocks A and B of masses $3m$ and $m,$ respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B immediately after the string is cut are, respectively,

Which one of the following statements is incorrect?

A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

Two bodies of mass $4$ kg and $6$ kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is:

A ball of mass $0.15$ kg is dropped from a height $10$ m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $\newline (g = 10$ m/s$^2)$ nearly:

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g = 10 m/s^2).

A horizontal force 10N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg, respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is: