The figure represents a solid uniform sphere of mass `M` and radius `R`. A spherical cavity of radius `r` is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

Options

A. non - uniform
B. towards the center of the cavity
C. directly proportional to `a`
D. All of these

Answer

C

Explanation

Gravitational field at any point inside the cavity is uniform (both in magnitude as well as direction). So, let us find its value at centre of cavity .
`E_(R ) = E_(T) - E_(C)` (at centre of cavity)
`R rarr `Remaining, `T rarr` total, `C rarr` cavity
`E_(R ) = E_(T)` (as `E_(C) = 0)`
`= ((GM)/(R^(3))) a` or `E_(R) prop a`