Question

# A uniform solid sphere of mass m and radius r is surrounded symmetrically by a uniform thin spherical shell of radius 2r and mass m. Choose the correct statement

A
The gravitational field at a distance of 1.5r from the centre is 29Gmr2
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B
The gravitational field at a distance of 2.5r from the centre is 825Gmr2
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C
The gravitational field at a distance of 1.5r from the centre is zero.
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D
The gravitational field between the sphere and spherical shell is uniform.
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Solution

## The correct option is B The gravitational field at a distance of 2.5r from the centre is 825Gmr2The net gravitational field at any point inside a spherical shell is zero So, at a distance 1.5r, field will only be due to solid sphere, which is given by, E=Gm(1.5r)2 ⇒E=49Gmr2 Hence option (a) and (c) are wrong. Also, the gravitational field intensity depends on the distance from the center, so it would not be uniform between the spherical shell and sphere. Hence, option (d) is also wrong. Gravitational Field intensity at a distance 2.5r will be due to both solid sphere and spherical shell, so E=Gm(2.5r)2+Gm(2.5r)2=825Gmr2 Hence, the option (b) is the correct alternative.

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