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Consider the solid S made of a material of constant density in the shape of a hemisphere of unit radius:

S = {(x, y, z) | x2 + y2 + z2 ≤ 1  z ≥ 0}.

Which of the following statements is true?

This question was previously asked in
CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. The centre of mass of S is at the origin
  2. The x-axis is a principal axis for S
  3. The moment of inertia tensor of S is not a diagonal matrix
  4. The z-axis is a principal axis for S

Answer (Detailed Solution Below)

Option 4 : The z-axis is a principal axis for S
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Detailed Solution

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The z-axis is a principal axis for S

Option (4) is correct

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