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 $m$ resting on a $\theta$ wedge of angle as shown in the figure. The wedge is given an acceleration a towards left. What is the minimum value of a due to external agent so that the mass $m$ falls freely ?

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is $g/8,$ then the ratio of the masses is :

Two masses of $10 \mathrm{kg}$ and $20 \mathrm{kg}$ respectively are connected by a massless spring as shown in the below figure. A force of $200 \mathrm{N}$ acts on the $20 \mathrm{kg}$ mass. At the instant shown the $10 \mathrm{kg}$ mass has acceleration $12 \mathrm{m}/{\mathrm{s}}^2$. What is the acceleration of $20 \mathrm{kg}$ mass ?

Three identical balls$1, 2, 3$are suspended on springs one below the other as shown in the figure. $OA$ is a weightless thread. The balls are in equilibrium

If the thread is cut, the system starts falling. Find the acceleration of all the balls at the initial instant

Acceleration of pulleys and blocks are as shown in the figure. All pulleys $\&$ strings are massless $\&$ frictionless magnitude of $a_A$ and $a_B$ are

The spring shown in the figure has a natural length of $1 \mathrm{m}$. What is the initial acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of the block when released?

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:-

A rocket is going upwards with accelerated motion. A man sitting in it feels his weight increased $5$ times his own weight. If the mass of the rocket including that of the man is $1.0\times {10}^4 \mathrm{kg}$. The force applied by rocket engine is $5\times {10}^4 \mathrm{N}$. $(\text{Take}\mathrm{ }g=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2})$

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