Question

A mass M is broken in two parts of mass m and (M-m) respectively. Relation between m and M so that the force of gravitational between the two parts is maximum is

• A. mM$=$2
• B. $m=\frac{M}{2}$
• C. $M=m^2$
• D. none of these

Answer 1

The correct option is B $m=\frac{M}{2}$

$F=G\frac{m(M-m)}{r^2}=km(M-m)where,k=\frac{G}{r^2}\therefore F=k[\frac{M^2}{2}-\frac{M^2}{2}+mM-m^2]=k[\frac{M^2}{4}-{(\frac{M}{4}-m)}^2]Fismaximum,when(\frac{M}{4}-m)=0\Rightarrow m=\frac{M}{2}$