Question

The escape velocity from earth is 11 km/sec. The escape velocity from a planet having twice the radius and the same mean density as that of the earth is?

• A. $11$
• B. $22$
• C. $33\sqrt{3}$
• D. $44\sqrt{3}$

Answer 1

The correct option is B $22$

Escape velocity $v_e=\sqrt{\frac{2G{M}_e}{R_e}}$

=$\sqrt{\frac{2G\left(\frac{4}{3}\pi \rho R_e^{2}d\right)}{R_e}}$

$\sqrt{2G(\frac{4}{3}\pi \rho R_e^2})d=>v_e\alpha R$

since density is same.

when radius is doubled escape velocity gets doubled

$2v_e=2\times 11=22\frac{km}{S}$