Question

A disc is rotating in a room. A boy standing on the edge of the disc of radius $R$ finds that the water droplets falling from the ceiling are always falling on his head. As one drop hits his head, the next one starts from the ceiling. If the height of the roof above his head is $H$, then angular velocity of the disc is

• A. $\sqrt{\frac{2gR}{H^2}}$
• B. $\pi \sqrt{\frac{2gH}{R^2}}$
• C. $\pi \sqrt{\frac{2g}{H}}$
• D. None of these

Answer 1

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


Height of ceiling above the boy's head = $H$ {Given}

Angular speed of boy = angular speed of disc $=\omega$

For water droplets to continously hit the head of the boy:
Time of flight of the droplet = Time period of revolving Disc
$\Rightarrow \sqrt{\frac{2H}{g}}=\frac{2\pi }{\omega }$
$\therefore \omega =\frac{2\pi }{\sqrt{\frac{2H}{g}}}=\pi \sqrt{\frac{2g}{H}}$