Applications of Second and Third Laws

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 ball is dropped from a high rise platform at, $t=0$ starting from rest. After $6 \mathrm{s}$ another ball is thrown downwards from the same platform with the speed $v$. The two balls meet at, $t=18 \mathrm{s}$. What is the value of $v$? (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

Two bodies, $\mathrm{A}$ (of mass $1 \mathrm{kg}$) and $\mathrm{B}$ (of mass $3 \mathrm{kg}$), are dropped from heights of $16 \mathrm{m}$ and $25 \mathrm{m}$, respectively. The ratio of the times taken by them to reach the ground is

A body falling freely from a given height $\text{'}H\text{'}$ hits an inclined plane in its path at a height $\text{'}h\text{'}$. As a result of this impact, the direction of the velocity of the body becomes horizontal. For what value of $\left(\frac{h}{H}\right)$ the body will take maximum time to reach the ground?

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 $2 \mathrm{kg}$ is lying on a smooth inclined plane as shown in the figure.The tension in the string will be (string is light and$g= 10 \mathrm{m}/{\mathrm{s}}^2$ )

A horizontal force $F= 200 \mathrm{N}$ pulls three masses $m_1= 5 \mathrm{kg}$, $m_2= 6 \mathrm{kg}$ and $m_3= 9 \mathrm{kg}$, lying on a frictionless table and connected by light strings. Find the tension in the string between blocks $m_1$ and $m_2$.

What is better to have one pulley or multiple pulleys?

Two masses 2 kg and 3 kg are attached to the end of the string passed over a pulley fixed at the top. Find acceleration of the blocks?

What happens when you put multiple pulleys together?

In a pulley block system,tension in a massless string is same at all points.

Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in the figure. What is the tension in the string connecting weights B and C ?

Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is 

Two blocks A and B of equal masses are in contact initially. The coefficients of friction between the inclined plane and the surface of A and B are ${\mu }_{1 and} {\mu }_2$​ respectively. The blocks will remain in contact and will fall with common acceleration_____

Why Crowning of pulley is done?

Two blocks of masses$6 \mathrm{kg}$ and $4 \mathrm{kg}$ are attached to the two ends of a massless string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the system will be :