# If length of a pendulum increases by 2% and accelaration due to gravity decreases by 2%, how is the time period of the pendulum affected?

Jul 25, 2017

Time period increases by about 2.02%

#### Explanation:

Time period of a simle pendulum is given by

$T = 2 \pi \sqrt{\frac{L}{g}}$

i.e. $T \propto \sqrt{\frac{L}{g}}$

if Length increases by 2%, it changes from $L \to 1.02 L$

and accelaration due to gravity decreases by 2%, it changes from $g \to 0.98 g$

Hence time will change by $\sqrt{\frac{1.02 L}{0.98 g}} = \sqrt{\frac{L}{g}} \times \sqrt{\frac{1.02}{0.98}}$

or $1.02020406 \sqrt{\frac{L}{g}}$

Hence time period increases by about 2.02%