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Q.

When the mass is doubled, the potential energy of a body becomes [[1]].

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Detailed Solution

When the mass is doubled, the potential energy of a body becomes twice.
We know that potential energy is the energy possessed by a body by virtue of its position. If the body of mass

m

, which is at the height of

h

, under the influence of gravity of the Earth

g

, the potential energy possessed by that body,

P = mgh . . . . . . . . . . . . . . (a)

From equation (a), we can understand that potential energy is directly proportional to the mass of the body and the height at which it is kept.
So, if we increase the value of

m

and

h

, the value of

P

also increases.
If we doubled the value of

m

, the new mass would be

2 m

.
Thus, new potential energy

P^{'} = 2 mgh

{\Rightarrow P}^{'} = 2 \times (mgh)

From (a), substituting the value of

P

We get

P^{'} = 2 P

Hence it is proved that if the mass is doubled, the potential energy of a body becomes twice.

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