Suppose you have two identical-looking metal spheres of the same size and the same mass. One of them is solid; the other is hollow. Describe a simple test that you could do to determine which is which.

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Chemistry

4 April, 21:02

Suppose you have two identical-looking metal spheres of the same size and the same mass. One of them is solid; the other is hollow. Describe a simple test that you could do to determine which is which.

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Eliana Kemp · Answer 1

We, apply equal torque to both spheres and measure their final angular acceleration.

Explanation:

The moment of Inertia of solid sphere will be (2/5) mr²

The moment of Inertia of hollow sphere will be (2/3) mr²

Thus, the moment of inertia of inertia of hollow sphere is greater than that of the solid sphere. Since, the torque is equal to the product of moment of inertia and angular acceleration.

Therefore, we design a test such that we apply the same amount of torque to both the spheres. Due to greater amount of moment of inertia the hollow sphere will acquire high angular acceleration, while solid sphere will acquire low angular acceleration.

Hence, by the measurement of final angular acceleration, we can determine, which sphere is which.