A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is `11kms^(-1)` , the escape velocity from the surface of the planet would be .......

Options

A. `1.1 kms^(-1)`
B. `11 kms^(-1)`
C. `110 kms^(-1)`
D. `0.11 kms^(-1)`

Answer

C

Explanation

`implies` Escape speed on earth `v_e = sqrt((2GM_e)/R_e)`
Escape speed on planet `v_p = sqrt((2GM_p)/R_p)`
but `M_p = 10 M_e and R_p = R_e/10`
`:. v_p =sqrt((2G(10M_e))/(R_e/10))= sqrt((100xx2GM_e)/R_e)`
`:. v_p = 10 xx v_e = 10 xx 11 = 110 kms^(-2)`