Question

If the distance between masses of two objects is increased by five units, by what factor would the mass of one of them have to be altered to maintain the same gravitational force? would there be an increase or a decrease in the mass? (Class 9 Gravitation Chapter)

Answer 1

Let M1 remain same.  M2 and distance d change.

Gravitational force:  Newtons' law:

   F = G M1 M2 / d²    = G M1  M2' / d' ²

   => M2' / M2 = (d' / d)²

given   d' = 5 d       ( or  d' = 6 d  perhaps, it not very clear.  Normally we say distance is increased by a factor of 5  or  increased to 5 times its value..  increased by 5 times means the new value is 6 times old value.)

  M2' = 25 * M2

So the mass of the second object has to be increased by a factor of 25.

Answer 2

Answer:

answer:16

Explanation:

The gravitational force b/w two bodies having mass M and m and separated by a distance r is denoted as

F = GMm/r2

When r is increased by factor 4 , then its effect will be indirectly proportional and in square , means G force will lessened by 16 times ….

For compensating this, one of the body needed to be heavier by 16 times

Hence answer is 16