The moment of inertia of a solid sphere of radius R about its diameter is the same as that of a disc of radius 2R about its diameter. The ratio of their masses is:
Correct answer: A. 4:5
- A. 4:5
- B. 5:8
- C. 4:1
- D. 2:1
Explanation
The moment of inertia (I) for a solid sphere about its diameter is given by the formula I = (2/5) m R2, while the moment of inertia for a disc about its diameter is I = (1/2) m (2R)2 = 2 m R2. Setting these equal gives:(2/5) msphere R2 = 2 mdisc R2By dividing through by R2 and rearranging, we find the mass ratio msphere / mdisc = 5 / 4. Thus, the ratio of their masses is 4:5, which is Option A. The other options do not satisfy the derived relationship, hence they are incorrect.
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