Question

A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$. The mass and the radius of the earth are, respectively, $M$ and $R$. $G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of $u$ so that the particle does not return back to earth is

• A. $\sqrt{\frac{2GM}{R}}$
• B. $\sqrt{\frac{2GM}{R^2}}$
• C. $\sqrt{2g{R}^2}$
• D. $\sqrt{\frac{GM}{R^2}}$

Answer 1

Answer: (A)

$GM=g{R}^2$
$V_e=\sqrt{2gR}=\sqrt{2\frac{GM}{R^2}}R=\sqrt{\frac{2GM}{R}}$.