Question

The ratio of escape velocity at earth (vc) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is

Answer 1

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Answer 2

Answer: The correct answer is $\frac{v_{e}}{v_{p}}=\frac{1}{2\sqrt{2}}$.

Explanation:

The expression for the escape velocity at the earth in terms of density is as follows;

$v_{e}=\sqrt{\frac{8}{3}\pi G\rho }$                           ....... (1)

The expression for the escape velocity at a planet in terms of density is as follows;

$v_{p}=\sqrt{\frac{8}{3}\pi G2\rho }$                        ......... (2)

Calculate the ratio of escape velocity at earth (vc) to the escape velocity at a planet (vp).

Divide the equation (1) by equation (2).

$\frac{v_{e}}{v_{p}}=\frac{\sqrt{\frac{8}{3}\pi G\rho }}{\sqrt{\frac{8}{3}\pi G2\rho }}$

$\frac{v_{e}}{v_{p}}=\frac{1}{2\sqrt{2}}$

Here, the correct answer is $\frac{v_{e}}{v_{p}}=\frac{1}{2\sqrt{2}}$.