Question

In space two point masses of mass $10kg$ each are fixed. The masses are separated by a distance $10m$. Another point mass of mass $1kg$ is to be projected from the point at midpoint of line joining the fixed masses such that it escapes to infinity. The minimum speed of the projection is

• A. $\sqrt{G}\frac{m}{s}$
• B. $\sqrt{2G}\frac{m}{s}$
• C. $\sqrt{8G}\frac{m}{s}$
• D. $\sqrt{6G}\frac{m}{s}$

Answer 1

The correct option is C $\sqrt{8G}\frac{m}{s}$


Let the minimum speed be $v$ for $1kg$ mass to just escape.
Then the mass has $v=0$ at $r=\infty$ since it just escapes. Therefore, $K_f=0$.

From conservation of mechanical energy
$K_i+U_i=K_f+U_f$
$\frac{1}{2}\left(1\right)v^2-2\frac{G\left(10\right)\left(1\right)}{5}=0-2\frac{G\left(10\right)\left(1\right)}{\infty }$
$\Rightarrow v^2=8G$
$\Rightarrow v=\sqrt{8G}$