First slide

Periodic Motion

Question

The pendulum of a certain clock has time period 2.04s. How fast or slow does the clock run during 24 hour ?

Easy

A

28.8 minutes slow
B

28.8 minutes fast
C

14.4 minutes fast
D

14.4 minutes slow

Solution

n₁ = Number of oscillations made by second pendulum in one day = $\large \frac{{86400}}{2}$
n₂ = Number of oscillations made by the given pendulum in one day = $\large \frac{{86400}}{{204}}$
$\large \therefore$ Number of osciallations lost per day = $\large = \,\left( {\frac{{86400}}{2} - \frac{{86400}}{{204}}} \right)$
So time lost per day = $\large = \,\left( {\frac{{86400}}{2} - \frac{{86400}}{{204}}} \right) \times 2.04\,\sec$
$\large = \,28.8\,\min$

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