Collisions

An object falls from a height of $10\text{ m}$ above the ground. After striking the ground it loses $50\%$ of its kinetic energy. The height upto which the object can rebound from the ground is:

If a rubber ball falls from a height $h$ and rebounds upto the height of $h/2$. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are:

A body is dropped on ground from a height '$h_1$ ' and after hitting the ground, it rebounds to a height '$h_2$'. If the ratio of velocities of the body just before and after hitting ground is 4, then percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is ____________.

A bullet of mass $0.1\text{ kg}$ moving horizontally with speed $400\text{ m s}^{-1}$ hits a wooden block of mass $3.9\text{ kg}$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\text{ m}$ before coming to rest. The coefficient of friction between the block and the surface is __________. (Given $g = 10\text{ m/s}^2$)

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms${}^{-1}$ gets embedded in it, then loss of kinetic energy will be:

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1: 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-

A block moving horizontally on a smooth surface with a speed of 40 ms${}^{-1}$ splits into two equal parts. If one of the parts moves at 60 ms${}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be x: 4 where x = ___________.

An object is dropped from a height h from the ground. Every time it hits the ground it loses 50% of its kinetic energy. The total distance covered as t $\to \infty$ is:

Two particles A and B, move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles A and B for their collision is

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{v}{3}.$ The second block's speed after the collision is

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is

(Take g = 10 m s${}^{-2}$)

A mass m moving horizontally (along the x-axis) with velocity $v$ collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2$v$. The final velocity of the combination is

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

A mass of 1 kg is thrown up with a velocity of 100 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity 25 m/s. The velocity of other part is (Take g = 10 ms${}^{-2}$)