which can be zero mass or weight?
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It is not possible for a body to have zero mass ( no body can exist without mass ) but a body can have zero weight..... Weight = Mass × Gravitational acceleration. At the center of the earth the gravitational acceleration is 0 so multiply 0 with mass and any no. multiplied with 0 is 0 so weight can be 0.
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Mass can never be zero but weight can be zero.
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