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You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

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No, It is impossible to screen the influence of gravitational force. This is mainly because unlike other forces the gravitational force acts on a body independent of the material medium or the status of the body on which it is acting or that of the body due to which it is present.

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