question_answer

A pendulum swings through an angle \[60{}^\circ \] and describes an arc 8.8 cm in length. Then, the length of pendulum is \[\left[ use\,\pi =\frac{22}{7} \right]\]

A) 8.40cm

B) 16.8cm

C) 4.20cm

D) 8.90cm

Correct Answer: A

Solution :

As per question, length of an arc of a sector of angle, \[\theta =60{}^\circ \] \[l=\frac{\theta }{360{}^\circ }\times 2\pi r\] \[\Rightarrow \,\,\,8.8=\frac{60}{360{}^\circ }\times 2\times \frac{22}{7}\times r\] \[\Rightarrow \,\,8.8=\frac{1}{3}\times \frac{22}{7}\times r\Rightarrow r=\frac{8.8\times 21}{22}\]\[\therefore \,\,\,\,\,r=8.40\,\,cm\]