$A$ boy is hanging from the branch of a tree as shown. For the tension in his arms to be maximum,the angle between his arms must be ............ $^o$.

Two identical weights of mass $M$ are linked by a thread wrapped around a frictionless pulley with a fixed axis. $A$ small weight of mass $m$ is placed on one of the weights. What is the reaction force between $m$ and $M$?

In the figure shown,both blocks are released from rest. Find the time taken for them to cross each other. (Assume $g = 10 \ m/s^2$)

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

In the pulley system shown,the mass of the ball is $1.2$ times greater than the mass of the rod. The length of the rod is $50 \,cm$. The ball is set on the same level as the lower end of the rod and then released. What is the acceleration of the rod with which it comes down (in $\,m/s^2$)? Assume the pulleys and threads are massless and friction is neglected. (Use $g = 10 \,m/s^2$)

Find the mechanical advantage for pulling mass $M$ by the person as shown in the figure.