Question

Length of second's pendulums is decreased by 1% then the gain or loss in time per day will be nearly

• A. 0.44 s
• B. 4.4 s
• C. 44 s
• D. 440 s

Answer 1

Answer: (D)

440 s

We need to calculate time lost $\left(\Delta T\right)$ in seconds per day $(T=24\times 60\times 60=86400s)$. We know that
$T=2\pi \sqrt{\frac{l}{g}}$
$\Rightarrow l=\frac{T^{2}g}{4{\pi }^2}$ .....$\left(I\right)$
$\Rightarrow \Delta l=\frac{2T\Delta Tg}{4{\pi }^2}$ .....$\left(II\right)$
now divide $\left(II\right)$ by $\left(I\right)$, We have
$\Rightarrow \frac{\Delta l}{l}=\frac{2\Delta T}{T}$
$\Rightarrow \Delta T=\frac{T}{2}\left(\frac{\Delta l}{l}\right)$
$\Rightarrow \Delta T=\frac{86400}{2}(-0.01)s=432s$
Out of all options we have, option 'D' is most close to it. so the correct answer is 'D'