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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
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Verified Answer
The correct answer is:
$\sqrt{\frac{2 G M}{R}}$
Escape velocity
$$
\begin{aligned}
& y_e=\sqrt{2 g R} \\
& y_e=\sqrt{\frac{2 G M}{R^2} R} \quad\left(\because G M=g R^2\right) \\
& y_e=\sqrt{\frac{2 G M}{R}}
\end{aligned}
$$
$$
\begin{aligned}
& y_e=\sqrt{2 g R} \\
& y_e=\sqrt{\frac{2 G M}{R^2} R} \quad\left(\because G M=g R^2\right) \\
& y_e=\sqrt{\frac{2 G M}{R}}
\end{aligned}
$$
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