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Standard XII

Physics

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A solid spher...

Question

A solid sphere of uniform density and mass $M$ has radius $4 m$ . Its centre is at the origin of the coordinate system. Two spheres of equal radii $1 m$ , with their centres at $P (0, - 2, 0)$ and $Q (0, 2, 0)$ respectively, are taken out of the solid leaving behind spherical cavities as shown if figure. What is the gravitational field at the origin of the coordinate axis?

\frac{31 G M}{1024}

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\frac{G M}{1024}

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31 G M

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Zero

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Solution

The correct option is D Zero
The mass distribution around the origin is symmetrical, the gravitational field due to diametrically opposite points will get cancelled.

Hence, the gravitational field at the origin will be zero.

Why this question?
To make students understand the gravitational field is a vector quantity and the direction should be accounted for while applying the principle of superposition.

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