A mass $M$ is held in place by an applied force $F$ and a pulley system as shown in the figure. The pulleys are massless and frictionless.

(a) Draw a free body diagram for each pulley.

(b) Find the tension in each section of rope $T_1, T_2, T_3, T_4$ and $T_5$.

(c) Find the magnitude of $F$.

In the figure shown, blocks $A$ and $B$ move with velocities $v_1$ and $v_2$ along horizontal direction. Find the ratio of $\frac{v_1}{v_2}$.

In the figure shown, the pulley is moving with velocity $u$. Calculate the velocity of the block attached with string.

If block $A$ has a velocity of $0.6 \mathrm{m} {\mathrm{s}}^{-1}$ to the right, determine the velocity of block $B$.

Velocities of blocks $A, B$ and pulley $p_2$ are shown in the figure. Find velocity of pulley $p_1$ and block $C$.

Find the acceleration of block  $A$ in terms of acceleration $\text{'}b\text{'}$ of wedge $B$ as shown in figure.

In the figure, the tension in the string between the points $1$ and $2$ is $60 \mathrm{N}$.

(a) Find the magnitude of the horizontal force ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ which must be applied to hold the system according to the position shown in figure.

(b) What is the weight of the suspended block?

A constant force $F=m_{1}g/2$ is applied on the block of mass $m_2$ as shown in the figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of $m_2$.

 A chain consisting of five links each with mass $100 \mathrm{gm}$ is lifted vertically with constant acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$ $\left(\uparrow \right)$ as shown. Find $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

(a) the forces acting between adjacent links.

(b) the force $F$ exerted on the top link by the agent lifting the chain.

(c) the net force on each link.