A thin, metallic spherical shell carries a charge Q . A point...

The point charge $q$ at the centre of the metallic spherical shell induces a charge $-q$ on the inner surface of the shell.

Since the charge $q$ is placed exactly at the centre, the induced charge $-q$ is uniformly distributed over the inner surface. The electric field produced by this uniformly distributed charge at the centre is zero.

Due to the property of electrostatic shielding in conductors, the electric field inside the cavity of the conductor due to the external charge $q_1$ and the charge on the outer surface of the shell is zero.

Therefore, the net electric field at the centre of the shell is zero, and the force acting on the charge $q$ is zero.