Question

3. Two billiard balls of mass 50 g moving in opposite
directions with speed of 16 ms -1 collide and
rebound with the same speed. What is the impulse
imparted by each ball to the other ?
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Answer 1

Question :

Two billiard balls of mass 50g moving in opposite directions with speed of 16 m/s collide and rebound with same speed . What is the impulse imparted by each ball on one other.

Given :

• Mass of two balls = 50 g

• Velocity of two balls = 16 m/s

To find :

The impulse imparted by the two balls.

Solution :

First let us convert the mass from g to kg.

Since, we know that :

1 g = 1000 kg.

50 g = (50/1000) kg

==> 50 g = 0.05 kg

Hence, the mass of the ball in kg is 0.05 kg.

We know the formula for Impulse,i.e,

$\boxed{\bf{Impulse = m(v - u)}}$

[Note :- Impulse is equal to the rate of change of momentum]

$:\implies \bf{\Delta\:P = m(v - u)}$

Where :-

• m = Mass of the body
• v = Final Velocity
• u = Initial Velocity

Here :-

• m = 0.05 kg
• v = 16 m/s
• u = (-16) m/s

[Note : The initial velocity will be taken as negative coz the body is moving in a opposite direction]

Now , using the above formula and substituting the values in it, we get :

$:\implies \bf{\Delta\:P = 0.05[16 - (-16)]}$

$:\implies \bf{\Delta\:P = 0.05 \times (16 + 16)}$

$:\implies \bf{\Delta\:P = 0.05 \times 32}$

$:\implies \bf{\Delta\:P = 1.6}$

$\boxed{\therefore \bf{Impulse\:(\Delta\:P) = 1.6\:kg\:ms^{-1}}}$

Hence, the impulse imparted by the two bodies is 1.6 kg m/s.