Question

Minute hand of a watch is $4\text{cm}$ long. How far does it's tip moves in $45\text{minutes}$? (use $\pi =3.14$)

• A. $6.28\text{cm}$
• B. $18.84\text{cm}$
• C. $12.56\text{cm}$
• D. $33.12\text{cm}$

Answer 1

The correct option is B $18.84\text{cm}$

In $60\text{minutes}$, the minute hand of a watch completes one revolution. Therefore, in $45\text{minutes}$, the minute hand turns through $\frac{45}{60}=\frac{3}{4}$ of one revolution.
$\therefore$ $\theta =\frac{3}{4}\times {360}^{\circ }={270}^{\circ }=\frac{3\pi }{2}\text{rad}$
Hence, the required distance travelled is given by
$l=r\theta =4\times \frac{3\pi }{2}\text{cm}=18.84\text{cm}$