Question

A ceiling fan has a diameter of the circle through the outer edges of the three blades of $120cm$ and rpm $1500$ at full speed consider a particle of mass $1g$ sticking at the outer end of a blade. Then force is?

Answer 1

In order to solve this question you have to remember the concept of centrifugal force. This force is defined as the outward throwing force which arises when the body is in a circular motion. In this question, the force experienced by the particle would be the centrifugal force.

Formula used:
The formula for centrifugal force is given by,

$F = mr{\omega ^2}$

Where $m$ is the mass of the object

$r$ is the radius at which the object is moving in a circular motion
$\omega$ is the angular velocity

Complete step by step solution:

It is given that the diameter of the circle through the outer edges of blades is given by,

$2R = 120cm$

So the radius is given by,

$R = 60cm$

Now convert it into a standard unit that is in meters, we get

$\Rightarrow R = 0.6m$

And the fan is moving with the frequency given by,

$f = 1500rpm$

On converting it into revolutions per seconds, we get

$\Rightarrow f = \left( {\dfrac{{1500}}{{60}}} \right)rps$

Mass of the particle sticking at the outer end of the blade is given by,

$m = 1g$

On converting it into a Standard unit that is in kilograms, we get

$\Rightarrow m = 0.001kg$

Now, calculate the angular velocity of the particle, that is given by the formula,

$\omega = 2\pi f$

Where $f$ is the frequency
On putting the value of frequency in the above given equation, we get

$\Rightarrow \omega = 2 \times 3.14 \times \left( {\dfrac{{1500}}{{60}}} \right)$

On further solving, we the value of angular velocity as,

$\Rightarrow \omega = 157rad/s$

Now, as we know that the formula for the centrifugal force is given by,

$F = mr{\omega ^2}$

On putting all the values we have,

$\Rightarrow F = 0.001 \times 0.6 \times {(157)^2}$

On further solving, we get the value of the centrifugal force as,

$\Rightarrow F = 14.78N$

Therefore, the particle experienced a force of $14.78N$.

Note: When a body is observed in a rotating frame of reference then a force antiparallel to the radius of the circular path being followed acts on the body. This force is called the centrifugal force. However the force necessary to keep a body in a circular path is called the centripetal force. These two forces balance each other.