Question

The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

• A. \(\frac{v}{3}\)
• B. \(\frac{2v}{3}\)
• C. \(\frac{3v}{4}\)
• D. \(\frac{9v}{4}\)

Answer 1

The Correct Option is C

The formula for escape velocity ($v_e$) is $v_e = \sqrt{\frac{2GM}{R}}$, with G representing the gravitational constant, M the planet's mass, and R its radius.

For a new planet, its mass is $M' = 9M$ and its radius is $R' = 16R$.

Consequently, the new escape velocity is $v_e' = \sqrt{\frac{2G(9M)}{16R}} = \frac{3}{4}\sqrt{\frac{2GM}{R}} = \frac{3}{4}v_e$.