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!!!

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