Question

A disc of radius R is rotating inside a room A boy standing near the rim of the disc, finds the water droplets falling from the ceiling is always hitting on his head. As one drop hits his head the next one starts from the ceiling. If height of the roof above his head is H. Angular velocity of disc is:

• A. $\pi \sqrt{\frac{2gR}{H^2}}$
• B. $\pi \sqrt{\frac{2gH}{R^2}}$
• C. $\pi \sqrt{\frac{2g}{H}}$
• D. $2\pi \sqrt{\frac{2g}{H}}$

Answer 1

The correct option is C $\pi \sqrt{\frac{2g}{H}}$

The time teken by $1$ drop to reach the head

$=\sqrt{\frac{2H}{g}}$

In this time disc completes $1$ rotation.

$\therefore$ time period of disc$=\sqrt{\frac{2H}{g}}$

$\therefore \frac{2\pi }{\omega }=\sqrt{\frac{2H}{g}}\Rightarrow \omega =\frac{2\pi }{\sqrt{\frac{2H}{g}}}=\pi \sqrt{\frac{2g}{H}}$