Question

Two particles having masses $m$ and $4m$ are separated by distance $l.$ The distance of the centre of mass from m is $x_{1}$ and $x_{2}$ is the distance of point at which gravitational field intensity is zero. Find the value of $\frac{x_{1}}{x_{2}}$

• A. $1$
• B. $2$
• C. $2.4$
• D. $3.6$

Answer 1

Answer: (C)

$x_{1}=\frac{4 m l}{5 m}=0.8 l$
$\frac{G m}{x_{2}^{2}}=\frac{4 G m}{\left(l-x_{2}\right)^{2}}$
$2 x_{2}+x_{2}=l$
$x_{2}=\frac{1}{3}$
$\frac{x_{1}}{x_{2}}=2.4$