A uniform solid sphere of mass ' m ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' 2r ' and mass ' m ' then the gravitational field (a) at a distance of 15 r from the centre is 2/9Gm/r² (b) at a distance of (2.5)r from the centre is 8/25Gm/r² (c) at a distance of (1.5)r from the centre is zero. (d) between the sphere and spherical shell is uniform.

Answer: (b). Inside the shell ( r 2r) total mass 2m acts as a point mass. (a) At 15r: E = (2Gm)/(225r²), not 2/9Gm/r². False. (b) At 2.5r: E = (2Gm)/(6.25r²) = 8/25Gm/r². True. (c) At 1.5r: E = (Gm)/(2.25r²) ≠ 0. (d) Between them E ∝ 1/r², not uniform. Both false. So the answer is (b).

A uniform solid sphere of mass ' m ' and radius ' r ' is surrounded… | MHT CET 2025 (23 Apr, Shift 1)

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Gravitational Field

A uniform solid sphere of mass ' $m$ ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' $2r$ ' and mass ' $m$ ' then the gravitational field

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Answer: (b)

Inside the shell ( $r < 2r$ ) only the sphere acts; outside it ( $> 2r$ ) total mass $2m$ acts as a point mass.
(a) At $15r$ : $E = \frac{2Gm}{225r^2}$ , not $\frac{2}{9}\frac{Gm}{r^2}$ . False.
(b) At $2.5r$ : $E = \frac{2Gm}{6.25r^2} = \frac{8}{25}\frac{Gm}{r^2}$ . True.
(c) At $1.5r$ : $E = \frac{Gm}{2.25r^2} \ne 0$ . (d) Between them $E \propto \frac{1}{r^2}$ , not uniform. Both false.
So the answer is (b).

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