The moon has a mass of `(1)/(81)` that of the earth and radius of `(1)/(4)` that of the earth. The escape speed from the surface of the earth is 11.2 km`//`s. The escape speed from surface of the moon is-

Options

A. 1.25`km//s`
B. `2.49km//s`
C. `3.7km//s`
D. `5.6km//s`

Answer

B

Explanation

On the earth
the escape speed is `Ve=sqrt((2GM)/(R_(e)))`
on the moon
the escape speed is `V_(m) =sqrt((2GM_(m))/(R_(m)))`
`(V_(m))/(V_(e)) =sqrt(((M_(m))/(M_(e)))((R_(e))/(R_(m))))`
`=sqrt(((1)/(81))((4)/(1)))=2/9`
`V_(m) =2/9 V_(e) = 2/9 xx 11.2 "km"//"sec"`
`=2.49 km sec^(-1)`