Gravitational field at the surface of a solid sphere is `1.5 xx 10^(-4) "N kg"^(-1)`. Find the gravitational field at a point situated inside the sphere at a distance equal to half of rhe radius of the solid sphere.

Options

A. `7.5xx10^(-4)"N kg"^(-1)`
B. `7.5xx10^(4)"N kg"^(-1)`
C. `70.5xx10^(-4)"N kg"^(-1)`
D. `=1.5xx10^(-7)"N kg"^(-1)`

Answer

A

Explanation

Let mass of the solid sphere is M and radius is R Its is given that
`E_("surface")=(GM)/(R^(2))=1.5xx10^(-4)`
`:. E(r=R//2)=(GM)/(R^(3))(R//2)`
`=(GM)/(2R^(2))=(1.5 xx 10^(-4))/(2)`
`=7.5xx10^(-4)"N kg"^(-1)`.