Question

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

• A. 86.4 s
• B. 43.2 s
• C. 72.5 s
• D. 32.5 s

Answer 1

Answer: (A)

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 $=24\times 3600s=86400s$
$\Delta T=\left(\frac{\Delta T}{T}\right)\times t$
$\Delta T=0.001\times 86400$
$\Delta T=86.4s$