# In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30s. The length of pendulum is measured by using a meter scale of least count 1mm and the value obtained is 55.0cm. The percentage error in the determination of g is close to (1) 0.7%(2) 0.2%(3) 3.5%(4) 6.8%

Given parameters

The formula for the acceleration due to gravity is

$g = frac{4pi ^{2}l}{T^{2}}$

where

l = 55cm

T = 30 sec/20

Δl = 1mm = 0.1cm

ΔT = 1/20 sec

Now to calculate percentage error in g

$frac{triangle g}{g} times 100% = left ( frac{triangle l}{l} + frac{2triangle T}{T} right )times 100%$ $frac{triangle g}{g} times 100% = left ( frac{0.1}{55} + frac{2left ( frac{1}{20} right )}{frac{30}{20}} right ) times 100%$ $frac{triangle g}{g} times 100% = 6.8%$