Question

A body is broken into two parts of masses $m_1$ and $m_2$ These parts are then separated by a distance r ,What is the value of $m_1/m_2$ so that the gravitational force has maximum possible value?

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $4:3$

Answer 1

The correct option is A $1:1$

Let the mass of the body is $m$

$\therefore m_1+m_2=m$

$F_G=\frac{G{m}_1{m}_2}{r^2}$

$F_G=\frac{G{m}_1\left(m-m_1\right)}{r^2}$

for $F_G\to max\frac{d\left(F_G\right)}{d{m}_1}=0$

$=\frac{G}{r^2}\left(m-2m_1\right)=0$

$=m_1=\frac{m}{2}$

$m_2=\frac{m}{2}$

$\therefore m_1/m_2=1:1$

Hence$,$ optin $\left(A\right)$ is correct$.$