Question

The escape velocity of a body from earths surface is $V_e$. The escape velocity of the same body from a height equal to $7R$ from the earths surface will be

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

Answer 1

The correct option is C $\frac{V_e}{2\sqrt{}2}$

We know that $V_e=\sqrt{\frac{2GM}{R}}$

From a height of $7R$, distance from center is $8R$.

conserving total energy,

$\frac{1}{2}m{V^{\prime }}_e^2-\frac{GMm}{8R}=0$

${V^{\prime }}_e=\sqrt{\frac{GMm}{4R}}=\frac{V_e}{\sqrt{8}}=\frac{V_e}{2\sqrt{2}}$