Question

A fan has 3 blades. The edges of two blades are $1m$ apart. A coin of mass $2g$ is placed on one of the blade edge. If the fan rotates with $600rpm$, the force experienced by the coin is nearly

• A. $3.1N$
• B. $4.6N$
• C. $5.2N$
• D. $2.8N$

Answer 1

Answer: (B)

$4.6N$

Centrifugal force $F_c$ acting on the particle is $m{\omega }^{2}r$, i.e.,
$F_c=m{\omega }^{2}r$ and $2r\sin {60}^{\circ }=1$
$\Rightarrow r=\frac{1}{\sqrt{3}}m$

$\omega =600rpm$ $=600\times \frac{\pi }{30}{s}^{-1}=20\pi /s$
$\Rightarrow F_c=0.002\times (20\pi {)}^2\times \frac{1}{\sqrt{3}}=4.55N\approx 4.6N$.