Gravitation in Depth

A planet of radius $R = \frac1{10} \times (\text{ radius of the Earth})$ has the same mass density as Earth. Scientist dig a well of dept $\frac R 5$ on it and lower a wire of same length and of linear mass density $10^{-3} \text{ kgm}^{-1}$ into it. If the wire is not touching anywhere, find the force applied at the top of the wire by a person holding in place.

Details and Assumptions:

• The radius of the Earth as $6\times 10^6\text{ m}$ .

• The acceleration due to gravity on Earth is $10\text { ms}^{-2}$ .