A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$. The mass and…
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
$\sqrt{\frac{2 G M}{R}}$
$\sqrt{\frac{2 G M}{R^2}}$
$\sqrt{2 g R^2}$
$\sqrt{\frac{2 G M}{R^2}}$
Solution
Escape velocity
$\begin{aligned}
& y_e=\sqrt{2 g R} \\
& y_e=\sqrt{\frac{2 G M}{R^2} R} \quad\left(\because G M=g R^2\right) \\
& y_e=\sqrt{\frac{2 G M}{R}}
\end{aligned}$