BM Sharma Solutions for Chapter: Newton's Laws of Motion I, Exercise 4: DPP

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.

A body of mass $m$ is placed over a smooth inclined plane of inclination $\mathrm{\theta }$ placed over a lift which is moving up with an acceleration $a_0$. The base length of the inclined plane is $L$. Calculate the velocity of the block with respect to the lift at the bottom if it is allowed to slide down from the top of the plane from rest.

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