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Mass M is split into two parts m and (M-...

Mass `M` is split into two parts `m` and `(M-m)`, which are then separated by a certain distance. What is the ratio of `(m//M)` which maximises the gravitational force between the parts ?

A

`1:4`

B

`1:3`

C

`1:2`

D

`1:1`

Text Solution

Verified by Experts

The correct Answer is:
C
If r is the distance between m and (M-m), the gravitational force will be
` F = G (m (M - m))/(r^2) = (G)/(r^2) (m M - m^2)`
For F to be maxim `(dF)/(dm) = 0` (as M and rare constants)
` therefore (d)/(dm) [ (G)/(r^2) (m M - m^2) ] = 0 " or " M - 2m = 0 " or " m/M = 1/2 (As (G)/(r^2) ne 0)`
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