Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is 10 `m//s^(2)` . Then the acceleration due to gravity on the surface of Mars is given by

Options

A. 0.2 `m//s^(2)`
B. `0.4 m//s^(2)`
C. `2 m//s^(2)`
D. `4 m//s^(2)`

Answer

D

Explanation

Given mass of earth =`10xxM_(m)`
where `M_(m)` = mass of mars
Radius of earth =2 `R_(m)`
where `R_(m)` = radius of mass and `g=(GM)/(R^(2))`
let gravity on the surface of mass is `g_(m)`
`therefore (g_(m))/(g_(E ))=(M_(m))/(M_(E ))xx(R_(E ))/(R_(m))^(2)`
`=10xx(M_(m))/(10M_(m))(2R_(m))/(R_(m))=4 m//s^(2)`