Question

If the length of second's pendulum is decreased by $2\%$, how many seconds it will loose per day ?

• A. $3927\text{s}$
• B. $3727\text{s}$
• C. $3427\text{s}$
• D. $864\text{s}$

Answer 1

The correct option is D $864\text{s}$

Time period of a simple pendulum,
$T\propto \sqrt{l}$
$\Rightarrow \frac{\Delta T}{T}=\frac{1}{2}\frac{\Delta l}{l}$
Given that length is decreased by $2\%$.
$\Rightarrow \frac{\Delta l}{l}=\frac{-2}{100}=-0.02$
$\Rightarrow \frac{\Delta T}{T}=\frac{1}{2}\times (-0.02)=-0.01$
This means loss in time per unit lapse of time for pendulum is $0.01\text{s}$
$\Rightarrow$Loss of time per day:
$\because 1\text{day}=24\times 3600=86400\text{s}$
$\Delta t_{\text{lost}}=86400\times 0.01=864\text{s}$