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What will be the period of oscillation for a simple pendulum if it makes $10$ oscillations in $10 seconds$ ?

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1 \sec

2 \sec

4 \sec

4.5 \sec

answer is B.

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Detailed Solution

The period of oscillation for a simple pendulum is

2 \sec

, if it makes

10

oscillations in

10 seconds

.
Given that,
The number of oscillations (n) =

10

Time taken (t)=

20 seconds

We know the relationship between frequency, oscillation and time, which is given by,
⇒

frequency (f) = \frac{number of osicllations (n)}{time taken (t)}

……………… (i)
Put the above values in equation (i) we get,

\Rightarrow frequency = \frac{10}{20}

f = 0.5 Hz

……………….. (ii)
As we know time period is inversely proportional to the frequency therefore,

time period = \frac{1}{frequency}

……………….. (iii)
Put the value of equation (ii) in equation (iii),

t = \frac{1}{0.5}

t = 2 seconds

Thus, the time period is

2 seconds

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