If a planet consits of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be (g on earth=`9.8m//sec^(2)`)

Options

A. `4.9m//sec^(2)`
B. `8.9m//sec^(2)`
C. `19.6m//sec^(2)`
D. `29.4m//sec^(2)`

Answer

C

Explanation

`g=(GM)/(R^(2)) :. g prop M/(R^(2))`
According to problem `M_(p)=(M_(e))/2` and `R_(p)=(R_(e))/2`
`:. (g_(p))/(g_(e))=((M_(p))/(M_(e)))((R_(e))/(R_(p)))^(2)=(1/2)xx(2)^(2)=2`
`implies g_(p)=2g_(e)=2xx9.8=19.6m//s^(2)`