Question

The escape velocity of a body from earth's surface is $v_c$. The escape velocity of the same body from a height equal to $7R$ from earth's surface will be

• A. $\frac{v_c}{\sqrt{2}}$
• B. $\frac{v_c}{2}$
• C. $\frac{v_c}{2\sqrt{2}}$
• D. $\frac{v_c}{4}$

Answer 1

Answer: (C)

$\frac{v_c}{2\sqrt{2}}$

Escape velocity of body from the earth's surface is $v_c=\sqrt{2gR}$
Escape velocity of a same body at a height $h$ from the earth's surface is
$v_c^{\prime }=\sqrt{\frac{2g{R}^2}{R+h}}=\sqrt{\frac{2g{R}^2}{R+7R}}$ [Given $h=7R$ ]
$=\frac{1}{2\sqrt{2}}\sqrt{2gR}=\frac{1}{2\sqrt{2}}{v}_c$.