Question

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

(1) v

(2) 2v

(3) 3v

(4) 4v

Answer 1

Correct option is (4) 4v

Escape velocity from the Earth's surface,

\(v_e = \sqrt{\frac{2GM}R}\)

\(= \sqrt{\frac{2G[\rho \times (4\pi R^3/3)]}{R}}\)

\(= \sqrt{\frac{8G\rho \pi R^2}3}\)

∴ v_e ∝ R (For same density)

\(\frac{v_1}{v_2} = \frac{R_1}{R_2}\)

⇒ \(\frac v{v_2} = \frac R{4R}\)

∴ v₂ = 4v

Answer 2

Option : (4) 4v