Question

A pendulum is 45 cm long. When it swings, it travels along the arc of a circle and covers a distance of 27.5 cm. Calculate the angle through which the pendulum travels.

Answer 1

Answer: The angle through which the pendulum travels = $35^{\circ}$.

Step-by-step explanation:

Formula: Length of arc: $l= r\theta$ , where r= radius ( in radians) , $\theta$ = central angle.

Given: Length of pendulum (radius) = 45 cm

Length of arc= 27.5 cm

Put these values in the formula, we get

$27.5=45\theta\\\\\Rightarrow\theta=\dfrac{27.5}{45}=\dfrac{275}{450}\\\\\Rightarrow\ \theta=\dfrac{11}{18}\text{ radians}$

In degrees ,

$\theta=\dfrac{11}{18}\times\dfrac{180}{\pi}=\dfrac{110\times7}{22} \ \ \ \ [\pi=\dfrac{22}{7}]$

$\theta=35^{\circ}$

Hence, the angle through which the pendulum travels = $35^{\circ}$.