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 $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$.

A lift weighing $1000 \mathrm{kg}$ is moving upwards with an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$. The tension in the supporting cable is $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The pulley arrangements of the figure. (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass $m$ is lifted up by attaching a mass $2m$ to the other end of the rope. In (b), $m$ is lifted up by pulling the other end of the rope with a constant downward force  $F=2mg$. The acceleration of $m$ in both cases is?

Two particles of mass $m$ each are tied at the ends of a light string of length $2a.$ The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F.$ As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x,$ is

The string between blocks of mass $m$ and $2m$ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass $2m$ and $m$ (immediately after cutting)

A block $P$ of mass $m$ is placed on a horizontal frictionless plane. A second block of mass $m$ is placed on it and is connected to a spring of spring constant $k,$ the two blocks are pulled by distance $A$. Block $Q$ oscillates without slipping. What is the maximum value of frictional force between the two blocks?

Three identical blocks of masses $m=2 \mathrm{kg}$ are drawn by a force $F=10.2 \mathrm{N}$ on a frictionless surface, then what is the tension (in $\mathrm{N}$) in the string between the blocks $B$ and $C$?

A player caught a cricket ball of mass $150 \mathrm{g}$ moving at a rate of $20 \mathrm{m} {\mathrm{s}}^{-1}$. If, the catching process is completed in $0.1 \mathrm{s}$, the force of the blow exerted by the ball on the hand of the player is equal to

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

An object of mass $2 \mathrm{kg}$ is dropped from height $10 \mathrm{m}$ on the surface of earth. The acceleration produced in the motion of earth by the object will be