Applications of Newton's Laws of Motion

The coefficient of static friction, ${\mu }_s$, between block $A$ of mass $2 \mathrm{kg}$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that, the two blocks do not move? The string and the pulley are assumed to be smooth and massless $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$.

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the magnitude and direction of the force of friction acting on $A.$

Two masses  $m_1=5 \mathrm{kg}$ and  $m_2=4.8 \mathrm{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? ($g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ )

A particle starts sliding down a frictionless inclined plane. If $S_n$ is the distance travelled by it from time $t=(n-1)$ $\sec$ to $t=n$ $\sec$, the ratio $\frac{S_n}{S_{n+1}}$ is

A block of mass $m,$ connected to a light string wrapped over a disc pulley of mass $2 \mathrm{m}$ and radius $2r,$ is being pulled by a constant horizontal force $\mathrm{F}$ as shown. Tangential acceleration of a point distant $r$ from the axis of pulley is (Assume that there is no slipping between the string and the pulley)

A block of mass $m$ is placed on a smooth inclined plane of inclination $\theta$ with the horizontal. The inclined plane is accelerated horizontally so that the block does not slide down. What is the vertical force exerted by the inclined plane on the block?

Ratio of tensions $T_1 \& T_2$ is:-

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

In which of the following cases the magnitude of the acceleration of the block $A$ will be maximum (Neglecting friction, the mass of pulley and string)

$\left(\mathrm{iii}\right)$

Two blocks are placed at rest on a smooth fixed inclined plane. A force $F$ acts on the block of mass $m_1$ and is parallel to the inclined plane, as shown in the figure. Both the blocks move up the incline. Then,

$\left(\mathrm{iii}\right)$ Find the normal reaction between the blocks of mass $m_1$ and $m_2$.

Find all the normal reactions $N_{\mathrm{AG}}$, $N_{\mathrm{AB}}$ and the accelerations of $A$ and $B$ (All surfaces are frictionless)

A helicopter of mass $2000 \mathrm{kg}$ rises with a vertical acceleration of $15 \mathrm{m} {\mathrm{s}}^{-2}$. The total mass of the crew and the passengers is $500 \mathrm{kg}$. Give the magnitude and direction of the action of the rotor of the helicopter on the surrounding air.

A force of $100 \mathrm{N}$ is applied on block $A$. The contact force between $B$ & $C$ is. $\left({\mathrm{m}}_{\mathrm{A}}={\mathrm{m}}_{\mathrm{C}}=50 \mathrm{kg}\&{\mathrm{m}}_{\mathrm{B}}=25 \mathrm{kg}\right)$

A monkey of mass $40 \mathrm{Kg}$ climbs on a massless rope which can stand a maximum tension of $500 \mathrm{N}$. In which of the following cases will the rope breaks? (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A ball is held at rest initially at position $\mathrm{A}$ by two light strings as shown in the figure. When the horizontal string is cut, the ball starts swinging as a pendulum with point $\mathrm{B}$ as its other extreme position. What is the ratio of the tension in the supporting string in position $\mathrm{B}$ to its value at $\mathrm{A}$ before the horizontal string was cut.



 

Taking friction to be absent everywhere, the magnitude of tension in the string connecting block$B$and block$C$ is?