Question

If the length of the pendulum in a pendulum clock increases by $0.1$%, then the error in time per day is :

• A. $86.4\text{s}$
• B. $43.2\text{s}$
• C. $8.64\text{s}$
• D. $4.32\text{s}$

Answer 1

The correct option is B $43.2\text{s}$

We know that in a pendulum clock, the time period ($T$) of the pendulum is equal to $1\text{s}$.
Also, $T=2\pi \sqrt{\frac{l}{g}}$
When the length is increased by $1$% :
$T^{\prime }=2\pi \sqrt{\frac{l+0.001l}{g}}$
$T^{\prime }=\sqrt{1.001}T$
Therefore, error in one day is :
$\Delta t=24\times 60\times 60(T^{\prime }-T)$
$\Delta t=24\times 60\times 60(\sqrt{1.001}-1)$
$\Delta t=43.2\text{s}$