Question

Percentage error in the measurement of time period of simple pendulum is 2% of the percentage error in the acceleration due to gravity is 4% then the percentage error in the length of the pendulum is

Answer 1

we have formula

g=4(pie)^2× length/(time)^2

so length will be g × (time)^2/4(pie)^2

lenght = 2× ( 2 % ) + 4 %

so percentage error in length will be 8 %.

hope it helps!

Answer 2

The error in the pendulum length is 8%

Explanation:

The acceleration due to gravity for pendulum is,

$g=4 \pi^{2} \frac{L}{T^{2}}$

From the above formula the length of the pendulum can be derived as,

$L=g \times \frac{T^{2}}{4 \pi^{2}} \rightarrow(1)$

On differentiating the above equation,

$d L=\left(d g \times \frac{T^{2}}{4 \pi^{2}}\right)+\left(2 \times \frac{T}{4 \pi^{2}} d T \times g\right) \rightarrow(2)$

Then by dividing eqn (2) by (1) we get,

$\frac{d L}{L}=\frac{d g}{g}+\frac{2 d T}{T}$

Where,

$\frac{d g}{g}=4 \%$

And

$\frac{d T}{T}=2 \%$

Thus,

$\frac{d L}{L}=4+(2 \times 2)=8 \%$

Thus, the error in the length of the pendulum is 8%