Why does the weight of a body of a finite mass m is zero at the centre of the Earth?

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Acceleration at depth d due to gravity is given by,

gd = g\((1-\frac{d}{R})\)

As, at centre of the Earth d = R ⇒ gd = 0.

Hence, the weight of a body of a finite mass m is zero at the centre of the Earth.

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