Question

The escape velocity from the earth is $11Km/s$. The escape velocity from a planet having twice the radius and same density as that of the earth is (in $Km/s$)

• A. $22$
• B. $15.5$
• C. $11$
• D. $7.77$

Answer 1

The correct option is D $7.77$

It is given that $Escapevelocity{V_{es}}_p=\sqrt{\frac{2GM}{R}}$

For earth escape velocity is

$V_E=\sqrt{\frac{2GM}{R}}$

$121=\frac{2GM}{R}.......\left(1\right)$

For any planet escape velocity is

$V_P=\sqrt{\frac{2GM}{R}}$

$V_p=\sqrt{\frac{2GM}{2R}}$

${V_p}^2=\frac{GM}{R}.......\left(2\right)$

Taking ratios of (1) and (2)

$\frac{121}{{V_p}^2}=\frac{2GM}{R}\frac{R}{GM}$

$\frac{121}{{V_p}^2}=2$

${V_p}^2=60.5m/s$

$V_p=7.77m/s$