Exercise-1

Two blocks, with masses $m_1=2.5 \mathrm{kg}$ and $m_2=14 \mathrm{kg}$, approach each other along a horizontal, frictionless track. The initial velocities of the blocks are $v_1=12.0 \mathrm{m} {\mathrm{s}}^{-1}$ to the right and $v_2=3.4 \mathrm{m} {\mathrm{s}}^{-1}$ to the left. The two blocks then collide and stick together. Which of the graphs could represent the force of block $1$ on block $2$ during the collision?

A small puck is sliding to the right with momentum ${\overrightarrow{p}}_i$ on a horizontal, frictionless surface, as shown in figure. A force is applied to the puck for a short time and its momentum afterward is ${\overrightarrow{p}}_f$. Which lettered arrow shows the direction of the impulse that was delivered to the puck?

A smooth sphere is moving on a horizontal surface with velocity vector $3\hat{i}+\hat{j}$ immediately before it hits a vertical wall. The wall is parallel to the vector $\hat{j}$ and the coefficient of restitution between the wall and sphere is $\frac{1}{3}$. The velocity vector of the sphere after it hits the wall is:-

A moving $2 \mathrm{kg}$ ball with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$ hits obliquely a stationary identical ball inelastically as shown. If the first ball move away with angle $\alpha =30°$ to the original path, find the total kinetic energy lost after the collision:-

A small body of superdense material, whose mass is twice the mass of the Earth but whose size is very small compared to the size of the Earth, starts from rest at a height $\mathrm{H}<<\mathrm{R}$ above the Earth's surface, and reach the, Earth's surface in time $t$. Then $t$ is equal to

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has the same mass. Length of the rod is $R$, where $\mathrm{R}$ is the radius of the Earth.

In an experiment with a beam balance an unknown mass $m$ is balanced by two known masses of $16\mathrm{kg}$ and $4\mathrm{kg}$ as shown in figure. The value of the unknown mass $m$ is :-

A uniform $"L"$ shaped rigid body $AOB$ of mass $m,$ where $AO=OB=l$ and $\angle AOB$ is a right angle, is hinged to a smooth joint at point $A$ of the body and can swing freely in a vertical plane. Initially, the body is released from rest with $AB$ horizontal. Find the maximum kinetic energy of the body.