$A$ mass $M$ is lowered by the help of a string at a constant acceleration of $\frac{g}{2}$ for a distance $x$. What is the work done by the string?

$A$ pendulum bob of mass $50 \,g$ is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately .......... $N$.

$A$ block of mass $m$ is pulled by a force of $40 \, N$ on a smooth horizontal surface as shown in the figure. The tension at the middle of the block is ........... $N$.

One end of a light string is fixed to a clamp on the ground and the other end passes over a fixed frictionless pulley as shown in the figure. It makes an angle of $30^{\circ}$ with the ground. The clamp can tolerate a vertical force of $40 \,N$. If a monkey of mass $5 \,kg$ were to climb up the rope,then the maximum acceleration in the upward direction with which it can climb safely is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?

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 $g = 10\, m/s^2$)