Consider two concentric spherical shells having masses M₁ , M₂ and radii R₁ , R₂ ( R₁ < R₂ ). Determine the force exerted by the system on a particle of mass m if it is positioned at a distance of (R₁ + R₂)/2 from the centre.

Step-by-step solution

The distance of the particle from the centre is r = R₁ + R₂ 2 . Since R₁ The gravitational field inside a uniform spherical shell is zero. Therefore, the force exerted by the outer shell of mass M₂ on the particle is zero. For a point outside a uniform spherical shell, the shell behaves as if its entire mass is concentrated at the centre. The force exerted by the inner shell of mass M₁ on the particle is: F = GM₁ m r^2 Substituting r = R₁ + R₂ 2 : F = GM₁ m ( R₁ + R₂ 2 )^2 = 4GM₁ m (R₁ + R₂)^2 The total force on th