Question

If the percentage increase in the length of the simple pendulum is 2% then find the percentage increase in its time period.

Answer 1

The formula for time period -

$T=2\pi \sqrt{\frac{L}{g}}=2\pi (\frac{L}{g}{)}^{\frac{1}{2}}$

Here 2, $\pi$, g have no dimensions. So we can eliminate them.

Now $\frac{\Delta T}{T}=\frac{1}{2}\times \frac{\Delta L}{L}$

By representing in percentage error

$\frac{\Delta T}{T}\times 100=\frac{1}{2}\times \frac{\Delta L}{L}\times 100$

$\frac{\Delta T}{T}$% = $\frac{1}{2}\times 2$%

$\frac{\Delta T}{T}$ % = 1 %

Hence the time period becomes 1 %