MCQ
- A$24 M R^2$
- ✓$32 M R^2$
- C$56 MR ^2$
- D$80 MR ^2$
✓
Answer
Correct option: B.
$32 M R^2$
(b) : Use parallel axis theorem,
$
\begin{aligned}
& I_A=\frac{2}{5} M R^2+\left(\frac{2}{5}+4\right) M R^2+\left(\frac{2}{5}+16\right) M R^2+\left(\frac{2}{5}+36\right) M R^2 \\
& I_A=\left(4 \times \frac{2}{5}+56\right) M R^2 \\
& I_B=\left(\frac{2}{5}+4\right) M R^2+\frac{2}{5} M R^2+\left(\frac{2}{5}+4\right) M R^2+\left(\frac{2}{5}+16\right) M R^2 \\
& I_B=\left(2 \times \frac{4}{5}+24\right) M R^2
\end{aligned}
$
Now, $I_A-I_B=(56-24) M R^2=32 M R^2$
$
\begin{aligned}
& I_A=\frac{2}{5} M R^2+\left(\frac{2}{5}+4\right) M R^2+\left(\frac{2}{5}+16\right) M R^2+\left(\frac{2}{5}+36\right) M R^2 \\
& I_A=\left(4 \times \frac{2}{5}+56\right) M R^2 \\
& I_B=\left(\frac{2}{5}+4\right) M R^2+\frac{2}{5} M R^2+\left(\frac{2}{5}+4\right) M R^2+\left(\frac{2}{5}+16\right) M R^2 \\
& I_B=\left(2 \times \frac{4}{5}+24\right) M R^2
\end{aligned}
$
Now, $I_A-I_B=(56-24) M R^2=32 M R^2$
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