Question

A uniform thin rod is hung vertically from one end and set into small amplitude oscillation. If the rod has a length of 2.6 m, this rod will have the same period as a simple pendulum of length ____ cm. Round your answer to the nearest whole number.

Answer 1

Answer:

Length of pendulum, l = 1.74 meters

Explanation:

The time period of simple pendulum is, $T=2\pi\sqrt{\dfrac{l}{g}}$

Where

l is the length of simple pendulum

The time period of  uniform thin rod is hung vertically from one end is, $T=2\pi\sqrt{\dfrac{2l'}{3g}}$

l' is the length of uniform rod, l' = 2.6 m

It is given that the rod and pendulum have same time period. So,

$2\pi\sqrt{\dfrac{l}{g}}=2\pi\sqrt{\dfrac{2l'}{3g}}$

After solving above expression, the value of length of the pendulum is, l = 1.74 meters. Hence, this is the required solution.