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

Three identical balls $A, B, C$ are suspended on springs one below the other as shown in the figure. $OA$ is a weightless thread. The balls are in equilibrium

 (a) If the thread is cut, the system starts falling. Find the acceleration of all the balls at the initial instant

(b) Find the initial accelerations of all the balls if we cut the spring $BC$, which is supporting ball $3$, instead of cutting the thread.