Question

The error in the measurement of length of a simple pendulum is $0.1\%$ and error in the time period is $2\%$. The possible maximum error in the quantity having dimensional formula $L{T}^{-2}$ is

• A. $1.1\%$
• B. $2.2\%$
• C. $4.1\%$
• D. $6.1\%$

Answer 1

The correct option is B $2.2\%$

Given,

Error $\%$ in time $=2\%=\frac{2}{100}=\frac{1}{50}=2\%$

Error $\%$ in length $=0.1\%$

Find $\%$ error in $\frac{1}{12}$

$\therefore$ as $\frac{△A}{A}=\left(\frac{△2}{2}\right)+\left(\frac{△Q}{Q}\right)$ if $A=\frac{t}{Q}$

Thus,

$\Rightarrow \%$ error $=\left(\frac{△L}{L}\right)+2\left(\frac{△T}{T}\right)$

$=\left(2\%\right)+2\left(.1\%\right)$

$=2\%+.2\%$

$=2.2\%$

Hence, the answer is $2.2\%.$