Question

The radius of the circle traced out by the second hand on a clock is 6.00 cm. In a time t the tip of the second hand moves through an arc length of 19.0 cm. Determine the value of t in seconds.

Answer 1

Answer:

30.29 s

Explanation:

We are given that

Radius=r=6 cm

Length of an arc=l=19 cm

We have to find the value of t in seconds.

$\theta=\frac{l}{r}$

Substitute the values then we get

$\theta=\frac{19}{6}=3.17 rad$

We know that

1 minute=60 seconds

In 60 seconds ,second hand makes an angle=$2\pi$radian

$2\pi$ radian made by second had in 60 sec.

1 radian made by second hand in $\frac{60}{2\pi}$ sec

3.17 rad made by second hand in $\frac{60}{2\pi}\times 3.17=\frac{60}{2\times 3.14}\times 3.17=30.29 s$

Hence, the value of t =30.29 s