Question

A solid sphere of radius R and mass M is rotating about its diameter. The moment of intertia of the solid sphere rotating about an axis at a distance \(\frac{R}{3}\) from the centre and parallel to that diameter is

• A. \(\frac{11}{15}MR^2\)
• B. \(\frac{13}{20}MR^2\)
• C. \(\frac{23}{45}MR^2\)
• D. \(\frac{47}{45}MR^2\)

Hint:

At the top, the water stays if gravity alone can supply the centripetal force.

Answer 1

The Correct Option is C

Step 1: Use speed at the top:
The least speed at the top is $v = \sqrt{gr}$, found from $\frac{mv^2}{r} = mg$.

Step 2: Convert to a period:
$T = \frac{2\pi r}{v} = \frac{2\pi r}{\sqrt{gr}} = 2\pi\sqrt{\frac rg}$ (B).

Final Answer:
$2\pi\sqrt{r/g}$. \[ \boxed{2\pi\sqrt{\frac{r}{g}}} \]