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Question

(B) The gravitational field $E$ at a distance $x$ from the centre of a system consisting of a solid sphere (mass $m$,radius $r$) and a concentric shel

Vedclass · Accepted Answer

at a distance of $2.5r$ from the centre is $\frac{8}{25} \frac{Gm}{r^2}$

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(B) The gravitational field $E$ at a distance $x$ from the centre of a system consisting of a solid sphere (mass $m$,radius $r$) and a concentric shell (mass $m$,radius $2r$) is given by the superposition of the fields of the two objects.For $r For $x = 1.5r = \frac{3}{2}r$,$E = \frac{Gm}{(1.5r)^2} = \frac{Gm}{2.25r^2} = \frac{4}{9} \frac{Gm}{r^2}$.For $x > 2r$,both act as point masses at the centre. $E = \frac{G(m+m)}{x^2} = \frac{2Gm}{x^2}$.For $x = 2.5r = \frac{5}{2}r$,$E = \frac{2Gm}{(2.5r)^2} = \frac{2Gm}{6.25r^2} = \frac{2Gm}{(25/4)r^2} = \frac{8}{25} \frac{Gm}{r^2}$.Thus,option $B$ is correct.

$A$ 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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