Question

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

• A. $\left(\frac{G M}{R}\right)^{1 / 2}$
• B. $\left(\frac{8 G M}{R}\right)^{1 / 2}$
• C. $\left(\frac{2 G M}{R}\right)^{1 / 2}$
• D. $\left(\frac{4 G M}{R}\right)^{1 / 2}$

Answer 1

Answer: (A)

Use $v^{2}=\frac{2 g h}{1+\frac{h}{R}}$ given $h = R$
$\therefore v=\sqrt{g R}=\sqrt{\frac{G M}{R}}$