Two billiard ball A and B each of mass `50g ` and moving in opposite direction with speed of `5ms^(-1)` each, collide and rebound with the same speed. The impulse imparted to each ball is

Options

A. `0.25"kgms"^(-1)`
B. `0.5"kgms"^(-1)`
C. `0.8"kgms"^(-1)`
D. `0.125"kgms"^(-1)`

Explanation

To solve the problem of calculating the impulse imparted to each billiard ball during the collision, we can follow these steps:

### Step 1: Understand the given data
- Mass of each ball (m) = 50 g = 0.05 kg (since 1 g = 0.001 kg)
- Initial speed of ball A (v_A) = 5 m/s (to the right)
- Initial speed of ball B (v_B) = -5 m/s (to the left, hence negative)

### Step 2: Calculate the initial momentum of each ball
- Initial momentum of ball A (p_A_initial) = m * v_A = 0.05 kg * 5 m/s = 0.25 kg·m/s
- Initial momentum of ball B (p_B_initial) = m * v_B = 0.05 kg * (-5 m/s) = -0.25 kg·m/s

### Step 3: Calculate the final momentum of each ball after the collision
Since both balls rebound with the same speed but in the opposite direction:
- Final speed of ball A (v_A_final) = -5 m/s
- Final speed of ball B (v_B_final) = 5 m/s

- Final momentum of ball A (p_A_final) = m * v_A_final = 0.05 kg * (-5 m/s) = -0.25 kg·m/s
- Final momentum of ball B (p_B_final) = m * v_B_final = 0.05 kg * 5 m/s = 0.25 kg·m/s

### Step 4: Calculate the change in momentum for each ball
- Change in momentum for ball A (Δp_A) = p_A_final - p_A_initial
= (-0.25 kg·m/s) - (0.25 kg·m/s) = -0.50 kg·m/s

- Change in momentum for ball B (Δp_B) = p_B_final - p_B_initial
= (0.25 kg·m/s) - (-0.25 kg·m/s) = 0.50 kg·m/s

### Step 5: Calculate the impulse imparted to each ball
Impulse (J) is equal to the change in momentum:
- Impulse on ball A (J_A) = Δp_A = -0.50 kg·m/s
- Impulse on ball B (J_B) = Δp_B = 0.50 kg·m/s

Since impulse is a vector quantity, the magnitude of the impulse imparted to each ball is:
- Impulse imparted to each ball = 0.50 kg·m/s

### Final Answer:
The impulse imparted to each ball is **0.50 kg·m/s**.