Question

An electric fan has blades on length $30cm$ as measured from the axis of rotation. If the fan is rotating at $1200rpm$, the acceleration of a point on the tip of the blade is about

• A. $1600m{s}^{-2}$
• B. $4740m{s}^{-2}$
• C. $2370m{s}^{-2}$
• D. $5055m{s}^{-2}$

Answer 1

The correct option is B $4740m{s}^{-2}$

Centripetal acceleration acts on the object along the radius towards the centre of the circular path.
When a point object is moving on a horizontal circular path with a constant speed, the direction of its velocity vector at an instant is changing with time. It means in a uniform circular motion the velocity vector of the object is changing with time. This indicates that the uniform circular motion is an example of accelerated motion.
Here, acceleration of a point at the tip of the blade
$=$ centripetal acceleration
$={\omega }^{2}R=(2\pi f{)}^{2}R$
$={(2\times \frac{22}{7}\times \frac{1200}{60})}^2\times \frac{30}{100}$
$=4740m/s^2$