Question

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

• A. $\bigg( \frac{GM}{R} \bigg) ^{1/2}$
• B. $\bigg( \frac{8GM}{R} \bigg) ^{1/2}$
• C. $\bigg( \frac{2GM}{R} \bigg) ^{1/2}$
• D. $\bigg( \frac{4GM}{R} \bigg) ^{1/2}$

Answer 1

Answer: (A)

$\bigg( \frac{GM}{R} \bigg) ^{1/2}$

Answer 2

Use $v^2 = \frac{ 2gh}{ 1+ \frac{h}{R}}$ given h = R.
$\therefore \, \, \, \, \, v = \sqrt{gR } = \sqrt{ \frac{ GM}{ R}}$.