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.

Find out the acceleration of the block $B$ in the following systems.

Find out the mass of block $B$ to keep the system at rest $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$.

A man of mass $60 \mathrm{kg}$ is standing on a weighing machine placed in a lift moving with velocity $v$ and acceleration $a$ as shown in the figure. Calculate the reading of the weighing machine in the following situations: $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

 (i) $a=0, v=0$

(ii) $a=0, v=2 \mathrm{m} {\mathrm{s}}^{-1}$

(iii) $a=0, v=-2 \mathrm{m} {\mathrm{s}}^{-1}$

(iv) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=0$

(v) $a=– 2 \mathrm{m} {\mathrm{s}}^{-2}, v=0$

(vi) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=2 \mathrm{m} {\mathrm{s}}^{-1}$

(vii) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=– 2 \mathrm{m} {\mathrm{s}}^{-1}$

(viii) $a=– 2 \mathrm{m} {\mathrm{s}}^{-2}, v=– 2 \mathrm{m} {\mathrm{s}}^{-1}$

What will be the reading of spring balance in the figure shown in following situations $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$.

 (i) $a=0, v=0$

(ii) $a=0, v=2 \mathrm{m} {\mathrm{s}}^{-1}$

(iii) $a=0, v=-2 \mathrm{m} {\mathrm{s}}^{-1}$

(iv) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=0$

(v) $a=– 2 \mathrm{m} {\mathrm{s}}^{-2}, v=0$

(vi) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=2 \mathrm{m} {\mathrm{s}}^{-1}$

(vii) $a=2 \mathrm{m} {\mathrm{s}}^{-2}, v=– 2 \mathrm{m} {\mathrm{s}}^{-1}$

(viii) $a=– 2 \mathrm{m} {\mathrm{s}}^{-2}, v=– 2 \mathrm{m} {\mathrm{s}}^{-1}$