Question

two ballsof masses inthe ratio 1:2 are droppedfrom same height .find:

1.ratio between their velocities when they strike the ground ,and

2. ratio of forces acting on them during motion

Answer 1

1. Let the masses of the balls be m and 2m which are in the ratio 1 : 2.

Initial PE of the ball of mass ‘m’ at the maximum height is = mgh

Final KE of the ball of mass ‘m’ just before hitting the ground is = ½ mu²

Now, mgh = ½ mu²

= > u = (2gh)^1/2

Initial PE of the ball of mass ‘2m’ at the maximum height is = (2m)gh

Final KE of the ball of mass ‘2m’ just before hitting the ground is = ½ (2m)uv²

Now, (2m)gh = ½ (2m)v²

= > v = (2gh)^1/2

Thus, the final velocity of the balls are same, i.e. u = v = (2gh)^1/2

So, the required ratio is, u : v = 1: 1

2. Force on the ball of mass ‘m’ is, F₁ = mg

Force on the ball of mass ‘2m’ is, F₂ = (2m)g

So, the ratio of force is, F₁ : F₂ = 1 : 2