Question

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

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

Answer 1

Answer: (C)

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

Using equation of motion for drop, $H=0+\frac{1}{2}g{t}^2$

$t=\sqrt{\frac{2H}{g}}$ which is equal to time period of the disc.

Let w be the angular velocity of disc, thus $t=\frac{2\pi }{w}$

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

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