In the figure, at the free end of the light string, a force $F$ is applied to keep the suspended mass of $18 \mathrm{kg}$ at rest. Then, the force exerted by the ceiling on the system (assume that the string segments are vertical and the pulleys are light and smooth) is $(g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$

A painter is applying force to raise himself and the box with an acceleration of $5\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$ by a massless rope and pulley arrangement as shown in the figure. The mass of the painter is $100\mathrm{ }\mathrm{kg}$ and that of box is $50\mathrm{ }\mathrm{kg}$. If $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, then,

A cylinder of mass $M$ and radius $R$ is resting on two corner edges $A$ and $B$, as shown in the figure. The normal reaction at the edges $A$ and $B$ are (neglect friction)

To paint the side of a building, a painter normally hoists himself up by pulling on the rope $A$, as shown in the figure. The painter and the platform together weigh $200\mathrm{ }\mathrm{N}$. The rope $B$ above the pulley can withstand $300\mathrm{ }\mathrm{N}$. Then,

Suppose you are sitting on an accelerating trolley car.

(i) Find the pseudo force acting on the block of mass $m$ placed on the trolley car if the block is placed (or moved) outside the trolley car and an external force $F$ acts in the horizontal direction.

(ii) Find the pseudo force acting on the block as viewed by the observer.

(iii) Find the acceleration of the block as seen by the observer.

A man of mass $m$ is standing on a lift which moves down with an upward acceleration $a$. Find the pseudo force acting on the man as observed by himself. Find the pseudo force acting on the man if the lift falls freely.

The block of mass $m$ is in equilibrium relative to the smooth wedge of mass $M$, which is pushed by a horizontal force $F$. Find the pseudo force acting on $\left(\mathrm{i}\right)$ $m$, $\left(\mathrm{ii}\right)$ $M$, as viewed by the observer sitting on the wedge. Will these pseudo forces be $\left(\mathrm{iii}\right)$ equal and opposite, action-reaction pairs? Explain.

A force $F$ is applied on block $A$ of mass $M$, so that the tension in the light string also becomes $F$, when block $B$ of mass $m$ acquires an equilibrium state with respect to block $A$. Find the force $F$. Give your answer in terms of $m, M$ and $g$.

A car is moving on a plane inclined at $30°$ to the horizontal with an acceleration of $10 \mathrm{m} {\mathrm{s}}^{-2}$ parallel to the plane upwards. A bob is suspended by a string from the roof. The angle, in $\mathrm{degrees}$, made by the string with the vertical is (assume that the bob does not move relative to car and $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$)