Question

Find the ratio of gravitational potential energy, if height of an object is doubled & mass is tripled. also find the ratio of work done by gravity in bringing the object to zero height in both cases meritnation

Answer 1

Answer:

Ratio of potential energy->6:1

Work done to bring height yo zero is `0'

Explanation:

Answer 2

1. The ratio of the gravitational potential energy when the object's height is doubled and mass is tripled is 1:6.

"Gravitational potential energy G.PE = mgh",  where 'g' is the acceleration due to gravity.

Case 1 - When the height is 'h' and mass is 'm'. Gravitational potential energy;

G.PE = m x g x h = 1(mgh)

Case 2 - When the height becomes '2h' and mass becomes '3m'. Gravitational potential energy;

G.PE = 3m x g x 2h = 6(mgh)

Therefore the ratio of Case 1: Case 2 = 1:6

2. The ratio of the work done by gravity to bring the object to zero height in both cases is 1:6.

"Work done by gravity  $W_{g}$ = -mg(Δh)",  where 'Δh' is the change in height and '-ve' sign indicates the fall in height.

Case 1 - When the mass is 'm' and height changes from 'h to 0'. Work done by gravity;

$W_{g}$ = -m x g x (h-0) = -1(mgh)

Case 2 - When the mass is '3m' and height changes from '2h to 0'. Work done by gravity;

$W_{g}$ = -3m x g x (2h-0) = -6(mgh)

Therefore the ratio of Case 1: Case 2 = 1:6