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.

A block of mas $2 \mathrm{kg}$ slides down the face of a smooth $45°$ wedge of mass $9 \mathrm{kg}$ as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.

In the figure shown, $A$ and $B$ are free to move, and they are released from rest. All the surfaces are smooth. $\left(0<\theta <90°\right)$