Energy in Collision

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. 

2. 

3. 

4. 

Q. In an inelastic collision of two bodies, the final kinetic energy is less than the initial kinetic energy of the system.

1. False
2. True

Q. The total energy of a system is always conserved irrespective of whether external forces act on the system.

1. False
2. True

Q. It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$ ​ ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$ ​ . The values of $p_d$ ​ and $p_c$ ​ are respectively.

1. (0, 0)
2. (0, 1)
3. (0.89, 0.28)
4. (0.28, 0.89)

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

Q. A ball of mass $4\text{kg}$ moving with velocity $4\text{m/s}$ collides with another identical ball at rest. The kinetic energy of the balls after collision is $\frac{7}{8}$ times of the original. Find the coefficient of restituton $\left(e\right)$.

1. $1$
2. $0.732$
3. $0.866$
4. $0.239$

Q. Two balls $A$ and $B$ of masses $2\text{kg}$ each are moving with speeds $1\text{m/s}$ and $2\text{m/s}$ on a frictionless surface. After colliding, ball $A$ returns back with speed $0.5\text{m/s}$, then the maximum potential energy of deformation is

1. $24\text{J}$
2. $4.5\text{J}$
3. $2.4\text{J}$
4. $45\text{J}$

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 railway carriage of mass $8000\text{kg}$ is moving with the speed of $54\text{km/hr}$ and collides with the another stationary carriage of same mass. Find the loss in kinetic energy in this process.

1. $600\text{kJ}$
2. $500\text{kJ}$
3. $350\text{kJ}$
4. $450\text{kJ}$