A mass M is split into two parts m and (.M-m.) , which are then separated by a certain distance. The ratio m:M which maximizes the gravitational force between the parts is

Question

A mass M is split into two parts m and (.M-m.) , which are then separated by a certain distance. The ratio m:M which maximizes the gravitational force between the parts is (A) 1:4 (B) 1:2 (C) 4:1 (D) 2:1

Tardigrade Admin · Accepted Answer

F=(G m (. M - m .)/x2); For maxima, (d F/d m)=(G/x2)(M - 2 m)=0 or (m/M)=(1/2)

Q. A mass $M$ is split into two parts $m$ and $(M - m)$ , which are then separated by a certain distance. The ratio $m : M$ which maximizes the gravitational force between the parts is

$1 : 4$

$1 : 2$

$4 : 1$

$2 : 1$

$F = \frac{G m ( M - m )}{x ^{2}};$ For maxima,
$\frac{d F}{d m} = \frac{G}{x ^{2}} (M - 2 m) = 0$
or $\frac{m}{M} = \frac{1}{2}$

Q. A mass M is split into two parts m and (M−m) , which are then separated by a certain distance. The ratio m:M which maximizes the gravitational force between the parts is

1:4

1:2

4:1

2:1