MCQ
If the value of moment of inertia of a solid sphere relative to its diameter is I, then the moment of inertia of the sphere relative to its tangent line will be:
- ✓$\frac{7}{2} I$
- B$\frac{5}{2} I$
- C$\frac{2}{5} I$
- D$\frac{1}{2} I$
✓
Answer
Correct option: A.
$\frac{7}{2} I$
A
$\begin{aligned} I & =\frac{2}{5} MR ^2 \\ MR ^2 & =\frac{5}{2} I \\ I _t & = I + MR ^2 \\ & = I +\frac{5}{2} I =\frac{7}{2} I \end{aligned}$
$\begin{aligned} I & =\frac{2}{5} MR ^2 \\ MR ^2 & =\frac{5}{2} I \\ I _t & = I + MR ^2 \\ & = I +\frac{5}{2} I =\frac{7}{2} I \end{aligned}$
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