A solid sphere of mass M and radius a is surr | vedclass

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(A) The gravitational field at a point outside a spherically symmetric mass distribution is equivalent to the field produced by a point mass equal to

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$\frac{GM}{3a^2}$

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(A) The gravitational field at a point outside a spherically symmetric mass distribution is equivalent to the field produced by a point mass equal to the total mass of the system located at the centre.The total mass of the system is the sum of the mass of the solid sphere and the mass of the spherical shell:$M_{total} = M + 2M = 3M$The distance from the centre is $r = 3a$.The formula for the gravitational field $g$ at a distance $r$ from a point mass $M_{total}$ is:$g = \frac{G M_{total}}{r^2}$Substituting the values:$g = \frac{G(3M)}{(3a)^2}$$g = \frac{3GM}{9a^2}$$g = \frac{GM}{3a^2}$

$A$ solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $3a$ from the centre will be

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