The mass of a planet is half that of the earth and the radius of the planet is one - fourth that of earth . If we plan to send an artificail satellite from the planet , the escape velocity will be ( escape velocity on earth `v_e= 11km-s^-1`)

Options

A. `11km-s^-1`
B. `1.5km-s^-1`
C. `15.55km-s^-1`
D. `7.78km-s^-1`

Answer

D

Explanation

Escape velocity
V_e = `sqrt(2GM)/R`
`Rightarrow (V_1)/V_2 =sqrt(Ma_1)/(M_2)xx (R_2)/(R_1)`
Since, `M_2= (M_1)/2, (R_2)= (R_1)/4`
`Rightarrow (V_1)/(11) = sqrt ((M_1)/((M_1)/2)xx(R_1/4)/R_1) Rightarrow v_1/11= 1/sqrt2`
`therefore v_1= (11)/ sqrt2 = 7.78kms^-1`