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  4. If the length of a clock pendulum increases by 0.2 % due to atmospheric temperature rise, then the loss in time of clock per day is

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Q. If the length of a clock pendulum increases by $0.2\%$ due to atmospheric temperature rise, then the loss in time of clock per day is

Oscillations

Solution:

Time perlod $=2 \pi \sqrt{\frac{I}{g}}$
$T \propto \sqrt{I} $
$\frac{T^{\prime}}{T} \propto \sqrt{\frac{I^{\prime}}{I}}$
$T=T \sqrt{\frac{1+/ \propto \Delta \theta}{l}}$
$T=T\left(1+\frac{1}{2} \propto \Delta \theta\right)[\alpha \Delta \theta=0.002] $
$\Delta T=T-T=\frac{1}{2} T \propto \Delta \theta=T \times 0.001$
Time lost in time $t$ is
$\Delta T=\frac{1}{2} \,\,t=1 $ day $=24 \times 3600\, s =86400\, s$
$\Delta T=\left(\frac{\Delta T}{T}\right) \times t $
$\Delta T=0.001 \times 86400 $
$\Delta T=86.4\, s$