A uniform sphere has radius ' R ' and mass ' M '. The magnitude of gravitational field at distances ' r ₁ ' and ' r ₂ ' from the centre of the sphere are ' E₁ ' and ' E₂ ' respectively. The ratio E₁: E₂ is ( r₁>R and r₂ < R )

Step-by-step solution

Gravitational Field Ratio Inside and Outside a Uniform Sphere To determine the ratio E₁:E₂ for a gravitational field at distances r₁ > R and r₂ Outside the sphere ( r > R ), the field is E_ out = GM r^2 , so E₁ = GM r₁^2 . Inside the sphere ( r The ratio is E₁ E₂ = GM r₁^2 GMr₂ R^3 = R^3 r₁^2 r₂ . This corresponds to option C.