Question
A clock regulated by a seconds pendulum keeps correct time. During summer the length of the pendulum increases to $1.01 m$. How much will the clock gain or lose in one day ? $g =9.8$ $\left.m / s ^2\right]$
✓
Answer
Data: $L =1.01 m , g =9.8 m / s ^2$
$
\begin{aligned}
T & =2 \pi \sqrt{\frac{L}{g}}=2 \times 3.142 \times \sqrt{\frac{1.01}{9.8}} \\
& =6.284 \sqrt{\frac{1.01}{9.8}}=2.017 s
\end{aligned}
$
The period of a seconds pendulum is 2 seconds. Hence, the given pendulum clock will lose $0.017 s$ in $2.017 s$ during summer.
$\therefore$ Time lost in 24 hours
$
=\frac{24 \times 3600 \times 0.017}{2.017} s =728.1 s
$
The given pendulum clock will lose 728.1 seconds per day during summer.
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