Question

The minute hand of a watch is $1.5cm$ along. How far does its tip move in $40$ minutes

Answer 1

We know that $l=r\theta$

Hence $r=1.5cm$

Now we know that minute hand make 1 revolution in 1-hour

Hence we can say minute hand completes ${360}^{\circ }$ in one hour

So degree complete in $1min=\frac{360}{60}$

So degree complete in $40min=\frac{360}{60}\times 40$$={240}^{\circ }$

Hence $\theta ={240}^{\circ }$

Radian measure $=\frac{\pi }{180}\times \theta$

$=\frac{\pi }{180}\times 240$

$=4\pi /3$

Now $l=r\theta$

$l=1.5\times 4\pi /3$

$l=0.5\times 4\pi$

$=2\pi$

$=2\times 3.14$

$l=6.28cm$