The escape Velocity from the earth is `11.2 Km//s`. The escape Velocity from a planet having twice the radius and the same mean density as the earth, is :

Options

A. `11.2 km//s`
B. `15.00 km//s`
C. `22.4 km//s`
D. `5.8 km//s`

Answer

C

Explanation

Escape velocity, `v_(e)=sqrt((2GM_(E))/(R_(E)))`
Also since earth is assumed spherical in shape its mass is given by
`M=4/3 pi R^(3)xxrho`
`:. v_(e)=sqrt((2G)/Rxx4/3piR^(3)rho)=Rsqrt(8/3 pi G rho)`
` :. v_(e) prop R` if `rho`=constant
Since the planet having double radius in comparison to earth, therefore the escape velocity becomes twice, i.e. `22km//s `