Find acceleration and tension in the string when two bodies are connected by a string over a pulley.

On a smooth table two blocks are placed two blocks in contact. A horizontal force of  $5 \mathrm{N}$ is applied on the $20 \mathrm{kg}$ block as shown. If this force is applied on the other side of $10 \mathrm{kg}$ block, The force with which  $20 \mathrm{kg}$ block will press the $10 \mathrm{kg}$ block is _____ $\mathrm{N}$ (up to two decimal places)

Three objects of the same mass $\mathrm{m}$ are tied as shown with an inextensible string. Find out the tension between $\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{B},\mathrm{C}$.

Three blocks are connected as shown and are on a horizontal smooth table. They are pulled to the right with a force $\mathrm{F}=50 \mathrm{N}$, If ${\mathrm{m}}_1=5\mathrm{kg}, {\mathrm{m}}_2=10\mathrm{kg} \mathrm{and} {\mathrm{m}}_3=15 \mathrm{kg}$. Calculate the tension ${\mathrm{T}}_1 \mathrm{and} {\mathrm{T}}_2$.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

The pulley arrangements in Figure are identical. The mass of the rope is negligible. If $\mathrm{m}$ is lifted up by pulling the other end of the rope with a constant downward force $F=2 mg$. Is the acceleration of $\mathrm{m}$ the same in both cases ?

Particles $A$ and $B$, of masses $0.4 \mathrm{kg}$ and $0.1 \mathrm{kg}$, respectively, are attached to the ends of a light inextensible string. Particle $A$ sits on a rough horizontal table and the string passes over a small smooth pulley at the edge of the table.

The system is released from rest and particle $B$ descends $1 \mathrm{m}$ in $2 \mathrm{s}$

Particle $B$ is now on the floor. Particle $A$ continues until it comes to rest, without having reached the pulley.

Find the total distance travelled by particle $A$.

In the given figure three blocks are connected by strings. Masses of blocks are  $m, 3m \mathrm{and} 5m$ respectively and they are pulled by force $F$ on a frictionless horizontal surface. The tension $P$ in the first string is $16 \mathrm{N}$.  Calculate tension $Q$ in the second string.

A roller of mass $500 \mathrm{kg}$ is attached by a light horizontal chain to a tractor of mass $1000 \mathrm{kg}$. The backward force of friction exerted by the ground is $1000 N$. If the system has a forward acceleration of $2.5{ \mathrm{ms}}^{-2}$, calculate the tension in the chain.

Two masses $8\mathrm{kg}, 12 \mathrm{kg}$ are connected by an inextensible string over a frictionless pulley. Find the Acceleration of the bodies and the tension in the string.

Two blocks $A$ and $B$ of masses $m \&2m$ respectively are held at rest such that the spring is in natural length. Find out the accelerations of
blocks $A$ and $B$ respectively just after release (pulley, string and spring are massless).

System shown in Fig. $7.64$ is in equilibrium and at rest. The spring and the string are massless, now the string is cut. The acceleration of mass $2 \mathrm{m}$ and $\mathrm{m}$ just after the string is cut will be

The pulley arrangement shown in the figure, the mass of the rope is negligible. Find the acceleration of mass $m$ in terms of acceleration due to gravity.

A block of metal of mass $2 \mathrm{kg}$ on a horizontal table is attached to a mass of $0.45 \mathrm{kg}$ by a light string passing over a frictionless pulley at the edge of the table.The block is subjected to a horizontal force by allowing the $0.45 \mathrm{kg}$ mass to fall. The coefficient of sliding friction between the block and table is $0.2$. Calculate the distance (in metres) the block would continue to move if, after $2$ seconds of motion, the string should break. ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

On a smooth horizontal surface a block A of mass $10 \mathrm{kg}$ is kept. On this block a second block B of mass $5 \mathrm{kg}$ is kept. The coefficient of friction between the two blocks is $0.4$. A horizontal force of $30 \mathrm{N}$ is applied on the lower block as shown. The force of friction between the blocks is 

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

The system shown in figure is in equilibrium and at rest. The spring and the string are massless, now the string is cut. The acceleration of mass $2 \mathrm{m}$ and $\mathrm{m}$ just after the string is cut will be