A cavity of the radius R 2 is made inside a solid sphere of radius R . The centre of the cavity is located at a distance R 2 from the centre of the sphere. The gravitational force on a particle of mass m at a distance R 2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of the cavity). [Here g = G M R 2 , where M is the mass of the sphere]

Question

A cavity of the radius R 2 is made inside a solid sphere of radius R . The centre of the cavity is located at a distance R 2 from the centre of the sphere. The gravitational force on a particle of mass m at a distance R 2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of the cavity). [Here g = G M R 2 , where M is the mass of the sphere], mg 2, 3 mg 8, mg 1 6, None of these

MARKS App · Accepted Answer

Gravitation field at mass m due to a full solid sphere E → 1 = - g 0 r → R = - g 0 r ^ 2 Gravitational field due to the cavity at mass m M ' = R 2 3 R 3 M ⇒ M ' = M 8 E → 2 = - - GM ' r ^ R 2 , = GM r ^ 8 R 2 = g 0 r ^ 8 E → net = - g 0 2 + g 0 8 r ^ = - 3 g 0 r ^ 8 ⇒ F → net = - 3 mg 0 r ^ 8

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