Two fielders, Dhoni and Virat catch fast balls having mass 200g moving with speed 225 km/h behind the wickets. Each one of them draws their hands backwards while catching the ball. Dhoni reduces the speed of the ball to zero in 5s while Virat catches it in 3s.
The ratio of change of momentum of the ball when it is caught by Virat to when caught by Dhoni will be
a)1:1
b)2:3
c)3:2
d)3:4
Answers
when it is caught by Virat to when caught by Dhoni will be
a)3.2
Given: Two fielders, Dhoni and Virat catch fast balls having mass 200g moving with speed 225 km/h behind the wickets. Each one of them draws their hands backwards while catching the ball. Dhoni reduces the speed of the ball to zero in 5s while Virat catches it in 3s.
To find: Ratio of change of momentum of the ball when it is caught by Virat to when caught by Dhoni
Explanation: Let the mass of the ball be m, initial velocity of the ball be u and final velocity of the ball be v.
m= 200 g
= (200/1000) kg (1 kg= 1000 g)
= 0.2 kg
u = 225 km/h
= 62.5 m/s (1 km/h = 5/18 m/s)
Since the ball comes to rest, the final velocity of the ball is 0.
v= 0
Momentum is the product of the mass of the body and its velocity.
Initial momentum
= m × u
= 0.2 × 62.5
= 12.5 kg m/s
Final momentum
= m × v
= 0.2 × 0
= 0
Change in momentum is the difference between the final momentum and the initial momentum.
When Dhoni catches the ball, change in momentum
= Final momentum- Initial momentum
= 0 - 12.5
= -12.5 kg m/s
When Kohli catches the ball, change in momentum
= Final momentum- Initial momentum
= 0 - 12.5
= -12.5 kg m/s
Clearly the change in momentum is same in both cases and does not depend on time.
Therefore, the ratio of change of momentum of the ball is option (a) 1:1.