If all the pulleys are massless and the string is ideal,find the reading of the spring balance.

$A$ man of mass $60 \ kg$ is standing on a platform of mass $40 \ kg$ as shown in the figure. What force should the man apply on the rope so that he accelerates upward with the platform with an acceleration of $2 \ m/s^2$ (in $N$)? (Take $g = 10 \ m/s^2$)

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 $\,ms^{-2}$)

Three masses $m_1 = 4 \text{ kg}$,$m_2 = 4 \text{ kg}$,and $m_3 = 6 \text{ kg}$ are suspended from a fixed smooth frictionless pulley as shown in the figure. The value of $T_1/T_2$ is . . . . . . . (Take $g = 10 \text{ m/s}^2$)

Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible?

Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............