Question

A 148 g ball is tied to a string. It is pulled to an angle of 7.2 ∘ and released to swing as a pendulum. A student with a stopwatch finds that 22 oscillations take 20 s .

Answer 1

ANSWER

First, we have to keep in mind that the period of swing of a simple gravity pendulum (our case) depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, , called the amplitude. It is independent of the mass of the ball. Thus, if the amplitude is limited to small swings, the period of a simple pendulum, the time taken for a complete cycle, will be:

(1)   to   

To use this formula, we have to keep in mind that the mass of the ball doesn't matter, and the original angle must be small; mainly .

Since 22 oscillations take 20 seconds, the period will be:

Then, solving the equation (1) for length gives:

   ANS.

Regards!!!