Question

The centres of a ring of mass m and a sphere

Answer 1

Given that,

Mass of ring = m

Mass of sphere = M

Radius = R

Distance = √8R

We need to calculate the intensity of gravitational field

Using formula of intensity

$E_{g}=\dfrac{Gmx}{\sqrt{(r^2+x^2)^\frac{3}{2}}}$

Put the value into the formula

$E_{g}=\dfrac{Gm\sqrt{8}R}{(R^2+8R^2)^{\frac{3}{2}}}$

$E_{g}=\dfrac{2\sqrt{2}Gm}{(9R^2)^{\frac{3}{2}}}$

$E_{g}=\dfrac{2\sqrt{2}Gm}{27R^2}$

We need to calculate the force of attraction  between the ring and the sphere

Using formula of attraction force

$F=M\times E_{g}$

Where, M = mass of sphere

E = intensity of gravitational field

Put the value into the formula

$F=\dfrac{2\sqrt{2}GmM}{27R^2}$

Hence, The force of attraction  between the ring and the sphere is $\dfrac{2\sqrt{2}GmM}{27R^2}$