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Standard XII

Physics

Ampere's Circuital Law

The figure re...

Question

The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius $r$ is at a distance $a$ from the centre of the sphere. The gravitational field inside the cavity is

non-uniform

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towards the centre of the cavity

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directly proportional to

a

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All of the above

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Solution

The correct option is D directly proportional to $a$
Gravitational field at any point inside the cavity is uniform (both in magnitude as well as direction). So, let us find its value at centre of cavity.
$E_{R} = E_{T} - E_{C}$ (at centre of cavity)
R $\to$ Remaining, T $\to$ total
C $\to$ cavity
So, $E_{R} = E_{T}$ (as $E_{C} = 0$ )
$= (\frac{G M}{R^{3}}) a$ or $E_{R} \propto a$

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The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius $r$ is at a distance $a$ from the centre of the sphere. The gravitational field inside the cavity is