A man of mass $60\ kg$ is standing on a platform of mass $40\ kg$ as shown in figure then what force man should apply on rope so that he accelerate up with the platform with acceleration of $2\ m/s^2$ ............ $N$

In the figure, mass of a ball is $\frac{9}{5}$ times mass of the rod. Length of rod is $1 \,m$. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod. (in $S$)

If the block $A$ & $B$ are moving towards each other with acceleration $a$ and $b$. Find the net acceleration of $C$.

If block $A$ has a velocity of $0.6\,m / s$ to the right, determine the velocity of block $B$.

An elevator accelerates upwards at a constant rate. A uniform string of length $L$ and mass $m$ supports a small block of mass $M$ that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$ . The acceleration of the elevator is

A uniform metal chain of mass $m$ and length ' $L$ ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $L -l$ ' is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........