Aball of mass m is dropped from rest from a height h and collides elastically with the floor, rebounding to its original height.

what is the magnitude of the average force applied by the floor on the ball during the time the ball is in contact with the floor?

(a) zero
(b) mg
(c) 2mg
(d) 4mg
(e) it cannot be determined without knowing the length of time that the ball is in contact with the floor.

It cannot be determined without knowing the length of time that the ball is in contact with the floor. Option E is correct.

Given information:

A ball of mass m is dropped from rest from a height h and collides elastically with the floor, rebounding to its original height.

Now, the ball will experience an impact or sudden change in momentum.

The impact, J, is defined as the change in the momentum, p, of the body.

Now, the average force acted on the body is the ratio of impact and total time of contact of the object with the surface.

Now, the change in momentum can be easily calculated using equations of motion but the time period of impact is not known.

So, we can't calculate the value of average force because it needs the time of impact to be known.

Therefore, it cannot be determined without knowing the length of time that the ball is in contact with the floor. Option E is correct.

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Explanation:

Given

mass m collides elastically with floor and jump to its original height I .e.velocity of rebound is same as the initial velocity

Impulse imparted by steel ball to the ground is given by the change in momentum of steel ball

and impulse is product of average force and time

so we need time to calculate the average force. So, option e is correct