Newton's Second Law 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

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

Two blocks of mass$2 \mathrm{kg}$ and$3 \mathrm{kg}$are arranged as shown and released from rest. Assuming string and pulley to be ideal, find the separation between them after$1 \sec$ [$g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

If acceleration of block $A$ in case $1$ is $a_1$ and in case $2$ is $a_2$, then $a_1:a_2$ is

One end of the carpet is bent back, then pulled backwards with constant unit velocity, just above the part of the carpet which is at rest on the floor. What is the minimum force needed to pull if the carpet has unit length and unit mass?

A smooth uniform rope is dragged by a force $F$ on a horizontal surface. The ratio $F$of tension$P$ and force $F$ is

In the system of pulleys shown what should be the value of $m_1$ such that $100 \mathrm{g}$ remains at rest: (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)