A mass M at rest is broken into two pieces having masses m and ( M − m ) . The two masses are then separated by a distance r The gravitational force between them will be the maximum when the ratio of

Question

A mass M at rest is broken into two pieces having masses m and ( M − m ) . The two masses are then separated by a distance r The gravitational force between them will be the maximum when the ratio of the masses [ m : ( M − m )] of the two parts is

TestHub · Accepted Answer

The gravitation force between two masses, F = r G m 1 ​ m 2 ​ ​ here, m 1 ​ = m and m 2 ​ = ( M − m ) F = r 2 G m ( M − m ) ​ ​ ∴ For maximum gravitational force, d m d F ​ = 0 ∴ d m d ​ [ m ( M − m )] = 0 By solving, we get m = 2 M ​ So, ( M − m ) m ​ = 1 1 ​

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