Question

If the distance between two masses is increased by a factor of 5,
by what factor would the mass of one of them have to be altered to maintain the same gravitational force?? would this be an increase or decrease in the mass??

Answer 1

Answer:

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:

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.

Explanation: