$A$ 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 masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in the figure. The ratio of the tensions $T_1/T_2$ is:

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ 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 $g = 10 \,m/s^2$)

$A$ $4 \text{ kg}$ mass is suspended as shown in the figure. All pulleys are frictionless and the spring constant $K$ is $8 \times 10^3 \text{ Nm}^{-1}$. The extension in the spring is $\left(g=10 \text{ ms}^{-2}\right)$.

Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from rest. The larger mass $(2\, kg)$ is stopped $1\, s$ after the system is set into motion and then released. Find the time elapsed before the string becomes tight again. (Take $g = 10\, m/s^2$)