Question 79 of 280

Let the moment of inertia of a hollow cylinder of length $30cm$ (inner radius $10cm$ and outer radius $20cm$ ), about its axis be $\text{I}$ . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $\text{I},$ is:

A$16cm$B$14cm$C$12cm$D$18cm$

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Answer: (A) $16cm$

Moment of inertia of a hollow cylinder whose inner radius id r and outer radius is R is given as
$I=\dfrac{m({R}^{2}+{r}^{2})}{2}$
$\dfrac{m\left({20}^{2}+{10}^{2}\right)}{2}=m{k}^{2}$

$K=\sqrt{\dfrac{400+100}{2}}; K=\sqrt{250}$

$K=5\sqrt{10} cm$