Question

# A uniform solid sphere of mass M and radius R is surrounded symmetrically by a uniform thin spherical shell of mass M2 and radius 2R. Then gravitational field at a distance of 52 R from the centre is

A
25GMR2 towards center
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B
25GMR2 away from the centre
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C
625GMR2 away from centre
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D
625GMR2 towards centre
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Solution

## The correct option is D 625GMR2 towards centre Gravitational field due to solid sphere at point P is given by, g1=GM(52R)2 g1=425GMR2 Gravitational field due to spherical shell at point P is given by, g2=G(M2)(52R)2 g2=225GMR2 Both g1 and g2 are pointing towards the common centre of the two spheres. Net gravitational field, gnet=g1+g2 gnet=425GMR2+225GMR2 gnet=625GMR2, towards the centre Hence, option (D) is the correct answer. Why this Question? Note: Newton's Shell theorem states that, for a hollow or solid sphere, if the point under considerarion is located at any outside point, then both the spheres can be treated as point masses located at their respective centres.

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