Question

The hour hand of a clock is $4\text{cm}$ long. What is the distance and displacement that its tip would cover in $12$ hours?

• A. $25.14\text{cm};0\text{cm}$
• B. $28.28\text{cm};25.14\text{cm}$
• C. $25.14\text{cm};28.28\text{cm}$
• D. $0\text{cm};25.14\text{cm}$

Answer 1

The correct option is A $25.14\text{cm};0\text{cm}$

A clock can be assumed as a circle. Then, the length of its hour hand is equal to the radius of the circle ($r$).
Given that the length of the hour hand, $r=4\text{cm}$
Here, the distance covered by the hour hand is the circumference of the circle.
$⟹$ The distance covered in $12\text{hr}$ (one complete round) = $2\pi r$
$=2\times \frac{22}{7}\times 4cm=25.14\text{cm}$
Therefore, the distance covered by the hour hand's tip in $12hr$ will be $25.14\text{cm}$.

After $12\text{hr}$, the hour hand comes back again to its initial position, i.e. if the hand is pointing at $5\left(AM\right)$, after $12\text{hr}$, it would again point at $5\left(PM\right)$. Therefore, the final and the initial positions of the hour hand would be the same in the span of $12\text{hr}$. Hence, there is no displacement, i.e. displacement $=0$