Chapter 7.1, Problem 62E

To determine

To determine the length of the arc formed.

Answer to Problem 62E

Length of the arc is around 2.44 cm

Explanation of Solution

Given information :

Length of the pendulum is 20 cm.

Angle on each side is $3^{\circ }30\text{'}$

Total angle is,

  $\begin{array}{c}2\left(3^{\circ }30\text{'}\right)=6^{\circ }60\text{'}\\ =6^{\circ }+{\left(\frac{60}{60}\right)}^{\circ }\\ =7^{\circ }\end{array}$

Now the length of the arc is given by, $\left(\text{string length}\right)\times \theta$

Hence we get,

  $S=20\left(7^{\circ }\right)$

Now we shall convert degree into radian, we get,

  $7^{\circ }\times \frac{\pi }{{180}^{\circ }}=\frac{7\pi }{{180}^{\circ }}$

  $\begin{array}{l}S=20\left(\frac{7\pi }{{180}^{\circ }}\right)\\ S\approx 2.44\text{ cm}\end{array}$