Q. 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) $\sqrt{2gR^{2}}$
B) $\sqrt{\frac{2GM}{R^{2}}}$
C) $\sqrt{\frac{2GM}{R}}$
D) $\sqrt{\frac{2gM}{R^{2}}}$
Explanation
(c) $GM = gR^{2}$
$u = \sqrt{2gR} = \sqrt{2\frac{GM}{R^{2}}R} = \sqrt{\frac{2GM}{R}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.