Figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface, holding a rope attached to a box $B$ . Boy pulls the rope with a constant force of $50\ N$ . (boy does not slip over the platform). The combined mass of platform $A$ and boy is $250\ kg$ and that of box $B$ is $500\ kg$ . The velocity of $A$ relative to the box $B$ , $5\ s$ after the boy on $A$ begins to pull the rope, will be ............ $m/s$

If pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4 \,kg$ and $8 \,kg$ respectively, then

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g / 8$, then the ratio of masses is

A rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.

A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as