Question

An open umbrella is held upright and rotated about the handle at a uniform rate of 21 revolution in $44s$. If the rim of the umbrella is a circle of $100cm$ diameter and the height of the rim above ground is $150cm$, then the drops of water spinning off the rim will hit the ground from center of umbrella, at a distance of:

• A. $200cm$
• B. $52cm$
• C. $172cm$
• D. $97cm$

Answer 1

The correct option is D $97cm$

Velocity of water drop,
$v=r\omega =0.5\times \frac{(2\pi \times 21)}{44}=1.5m{s}^{-1}$
Time taken to reach ground, $t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 1.5}{9.8}}=0.55s$
Range of drop, $x=vt=1.5\times 0.55=0.83m$
$\therefore$ distance: $R=\sqrt{r^2+x^2}=\sqrt{{0.5}^2+{0.83}^2}=0.97m$$=97cm$