A tunnel is dug along a diameter of the earth then the force on a particle of mass m placed in the tunnel at a distance R from the surface is equal to ______ where R is the radius of the earth.

Gravitational force is the force of attraction between any two objects having some mass. It is given by:
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$

Where M and m are the masses of the objects, r is the distance between them and G is the universal gravitational constant having the value of 6.67 X 10^-11 Nm²/kg².
Since the particle of mass m is placed at distance r of the tunnel, we can say that the particle is placed at the centre of the earth. At the centre of the earth, the gravitational force on the object will be zero as particles present on both sides will exert equal and opposite force on the particle at the centre and cancel out each other's gravitational force.
Hence option c is the correct answer.