Ncert Exercises & Solutions

Two billiard balls A and B, each of mass 50g and moving in opposite directions with a speed of 5 m/s each, collide and rebound at the same speed. If the collision lasts for $10^{- 3}$ s,

(a) The impulse imparted to each ball is 0.25 $k g - m s^{- 1}$ and the force on each ball is 250 N

(b) The impulse imparted to each ball is 0.25 $k g - m s^{- 1}$ and the force exerted on each ball is 25 x $10^{- 5}$ N

(c) The impulse imparted to each ball is 0.5 N-s

(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Which of the following statement(s) is/are true?

1. (a, c)

2. (a, b)

3. (c, d)

4. (b, c)

(3)

Hint: Apply the concept of conservation of momentum.

Step 1: Find the final velocities of the balls.

m_{1} = m_{2} = 50 (g) = \frac{50}{1000} k g = \frac{1}{20} k g

\begin{array}{l} Initial velocity (u) = u_{1} = u_{2} = 5 m / s \\ Final velocity (v) = v_{1} = v_{2} = - 5 m / s \\ Time duration of collision = 10^{- 3} s \\ Change in linear momentum = m (v - u) \end{array}

\begin{array}{l} = \frac{1}{20} [- 5 - 5] = - 0 .5 N - s \\ Force = \frac{Impulse}{Time} = \frac{Change in momentum}{10^{- 3} s} \\ = \frac{0 .5}{10^{- 3}} = 500 N \end{array}

Impulse and force are opposite in directions.

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