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 $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$) 

A wedge of height $h$ is released from rest with a light particle $P$ placed on it, as shown. The wedge slides down an incline which makes an angle $\text{θ}$ with the horizontal. If the surfaces are smooth, $P$ will reach the surface of the incline in time.

A cylinder rests in a supporting carriage, as shown. The side $AB$ of the carriage makes an angle $30°$ with the horizontal and the side $BC$ is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with a horizontal acceleration $a$. The magnitude of the normal reactions exerted by sides $AB$ and $BC$ of the carriage on the cylinder is $N_{\mathrm{AB}}$ and $N_{\mathrm{BC}}$, respectively (neglect friction everywhere). Then, as the magnitude of acceleration $a$ of the carriage is increased, choose the correct statement.

A ball is suspended on a thread from the ceiling of a car. The brakes are applied and the speed of the car changes from $5 \mathrm{m} {\mathrm{s}}^{-1}$ to $\frac{5}{3} \mathrm{m} {\mathrm{s}}^{-1}$, during a time interval of $3 \mathrm{s}$. Find the angle at which the thread with the ball, will deviate from the vertical.