Question

If the length of a seconds pendulum is increased by $2$% then what is loss and gain in a day?

• A. losses $764s$
• B. losses $924s$
• C. gains $236s$
• D. losses $864s$
• E. gains $346s$

Answer 1

Answer: (D)

losses $864s$

$T_0=2\pi \sqrt{\frac{l}{g}}{T}^1=2\pi \sqrt{\frac{l+l\times 2/100}{g}}\frac{T_0}{T^1}=\frac{\sqrt{100}}{\sqrt{102}}{T}^1=\frac{\sqrt{102}}{\sqrt{100}}{T}_0{T}^1=1.0099T_0\approx 1.01T_{0}Loss=(1.01-1)T_0=0.01T_0$

In one second, it looses $0.01sec$

$\Rightarrow$ Total time loose in one day$=(0.01\times 24\times 3600)seconds=864seconds$