Question

Velocity of a body of mass m moving with velocity v is reduced to half of its previous value. What is its new momentum?

Answer 1

Answer:

Explanation:

Let a body of mass m and velocity v is brought to test in time t.

Initial momentum = mv

Final momentum = m× 0 = 0 ( as the ball is brought to test its velocity is zero)

Change in momentum = final momentum - initial momentum= 0 - mv

Time in which ball is brought to rest = t

Rate of change in momentum = - m v/t

Force F = Rate of change of momentum =- mv/t

Impulse = Force F × t = change in momentum = -mv

When the time in which the ball is brought to rest is halved, there is no change in,

Initial momentum, it remains m v

Final momentum, it remains zero

Change in momentum, it remains - m v.

The only change is in the rate of change of momentum, which is doubled when the time is halved. Though impulse (=change in momentum) does not change, the force required is doubled.