Energy in Collision

Q. A ball is thrown up from the earth by a person and then caught by him on its return. When the ball falls towards the earth, the ratio of kinetic energies gained by the ball $\left(K_B\right)$ and the earth $\left(K_E\right)$ is

1. $\frac{K_E}{K_B}=\text{zero}$
2. $\frac{K_E}{K_B}=\frac{m_E}{m_B}$
3. $\frac{K_E}{K_B}=\frac{m_B}{m_E}$
4. $\frac{K_E}{K_B}=\text{Infinite}$

Q.

A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force, applied by the hand. Consider g = 10 m/$s^2$

1. 16 N

2. 20 N

3. 4 N

4. 22 N

Q. In an event of head-on elastic collision between two particles, which of the following statements given below is true?

1. Transfer of energy between the particles is maximum when their mass ratio is unity.
2. Transfer of energy between the particles is maximum when their mass ratio is less than one.
3. Transfer of energy between the particles is maximum when their mass ratio is greater than one.
4. Transfer of energy is maximum and is independent of masses.

Q. In an event of head-on elastic collision between two particles, which of the following statements given below is true?

1. Transfer of energy between the particles is maximum when their mass ratio is unity.
2. Transfer of energy between the particles is maximum when their mass ratio is less than one.
3. Transfer of energy between the particles is maximum when their mass ratio is greater than one.
4. Transfer of energy is maximum and is independent of masses.

Q. A tennis ball is dropped on a horizontal smooth surface. It bounces back after hitting the surface. The force on the ball during the collision is proportional to the degree of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to scale.

1. 
2. 
3. 
4. 

Q. A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2\text{m}$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle ${45}^{\circ }$ with respect to the original direction.
The speed of each of the moving particle will be

1. $\sqrt{2}v$
2. $\frac{v}{\sqrt{2}}$
3. $\frac{v}{\left(2\sqrt{2}\right)}$
4. $2\sqrt{2}v$

Q. A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2\text{m}$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle ${45}^{\circ }$ with respect to the original direction.
The speed of each of the moving particle will be

1. $\sqrt{2}v$
2. $\frac{v}{\sqrt{2}}$
3. $\frac{v}{\left(2\sqrt{2}\right)}$
4. $2\sqrt{2}v$

Q.

Two blocks of mass m₁ and m₂ interconnected with a spring of stiffness 'k' are kept on a smooth horizontal surface. Which of the following ratios are correct, if the spring was extended and released?

(Where X = displacement, v = speed, P = momentum, a = acceleration, all relative to the surface, KE = kinetic energy, F = force.)

1. $\frac{F_1}{F_2}=1\&\frac{X_1}{X_2}=1$

2. $\frac{v_1}{v_2}=\frac{m_2}{m_1}\&\frac{K{E}_1}{K{E}_2}=\frac{m_2}{m_1}$

3. $\frac{P_1}{P_2}=1\&\frac{K{E}_1}{K{E}_2}=\frac{m_1}{m_2}$

4. $\frac{X_1}{X_2}=\frac{m_2}{m_1}\&\frac{a_1}{a_2}=\frac{m_1}{m_2}$