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

Answer 1

Answer: (B)

$\sqrt{ \frac{ 2GM}{R}}$

Answer 2

$v _{\text {escape }}=\sqrt{\frac{2 GM }{ R }}$
Escape velocity from earth surface.