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.

Man $A$ of mass $60 \mathrm{kg}$ pushes the other man $B$ of mass $75 \mathrm{kg}$ due to which man $B$ starts moving with acceleration $3 \mathrm{m} {\mathrm{s}}^{-2}$. Calculate the acceleration of man $A$ at that instant.

Find the acceleration of the $6 \mathrm{kg}$ block in the figure. All the surfaces and pulleys are smooth. Also the strings are inextensible and light. [Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

A painter of mass $M$ stands on a platform of mass $m$ and pulls himself up by two ropes which hang over pulley as shown. He pulls each rope with the force $F$ and moves upward with uniform acceleration $a$. Find $a$.

Three monkeys $A, B$ and $\mathrm{C}$ with masses of $10, 15 \mathrm{and} 8 \mathrm{kg}$ respectively are climbing up and down the rope suspended from $D$. At the instant represented, $A$ is descending the rope with an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2} \mathrm{and} C$ is pulling itself up with an acceleration of $1.5 \mathrm{m} {\mathrm{s}}^{-2}$. Monkey $B$ is climbing up with a constant speed of $0.8 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate the tension $T$ in the rope at $D. (g=10 \mathrm{m} {\mathrm{s}}^{-2})$

An object of mass $2 \mathrm{kg}$ moving with constant velocity $10\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$ is seen in a frame moving with constant velocity $10\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$. What will be the value of ‘pseudo force’ acting on object in this frame.

In the adjoining figure, a wedge is fixed to an elevator moving upwards with an acceleration $a$. A block of mass $m$ is placed over the wedge. Find the acceleration of the block with respect to the wedge. Neglect friction.