Question

A simple pendulum is found to vibrate 50 times with 200s. When 1.5m of its length is reduces to a certain length, it vibrates 50 times in 175s. Find the original length of the pendulum.

Answer 1

$$T_1=2\pi\sqrt{\frac{l}{g}}=\frac{100}{50}=2\ s\\ T_2=2\pi\sqrt{\frac{l-d}{g}}=\frac{50}{50}=1\ s\\ \sqrt{\frac{l-d}{l}}=0.5\\l=\frac{4}{3}d=2\ m$$