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25 January, 13:31

I hand you two spheres. They have the same mass, the same radius, and the same exterior surface. I claim one is a solid sphere and the other is hollow. Can you determine which is which without cutting them open?

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  1. 25 January, 14:02
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    Between two spheres of equal masses having equal radius, the one which is hollow will have less moment of inertia and therefore less radius of gyration (k)

    When they are allowed to roll over an inclined plane, they will have acceleration as follows

    a = gsinθ / (1 + k²/r²)

    For hollow sphere, k is less. therefore denominator is less and acceleration is more.

    in other words, hollow sphere will have greater acceleration. So it will reach the bottom of an inclined surface in lesser time if allowed to roll over it.

    This is how we can identify a hollow sphere without breaking it open.
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