A lift is going up. The total mass of the lift and the passenger is $1500\, kg$. The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $t = 11^{th}\, sec$ will be ............ $N$

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of $30^o$ with the ground. A monkey of mass $5\,kg$ climbs up the rope. The clamp can tolerate a vertical force of $40\,N$ only. The maximum acceleration in upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10\, m/s^2$)

What should be the minimum force $P$ to be applied to the string so that block of mass $m$ just begins to move up the frictionless plane.

Find the acceleration of $3\,kg$ mass when acceleration of $2\,kg$ mass is $2\,ms ^{-2}$ as shown in figure.

A man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth  horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the  platform, then recoil velocity of platform is

A block of mass $m$, is kept on a wedge of mass $M$, as shown in figure such that mass $m$ remains stationary w.r.t. wedge. The magnitude of force $P$ is