Question

Spring constant $k$ is measured as a ratio of force applied on it to the elongation produced in it. Time period of a spring mass system is given as $T=2\pi \sqrt{\frac{m}{k}}$. If error in measurement of elongation produced in a spring for a given force is $+4\%$ and mass is measured with a negative error of $2\%$. Then percentage error in calculation of time period will be nearly

• A. $1\%$
• B. $3\%$
• C. $6\%$
• D. $2.8\%$

Answer 1

The correct option is A $1\%$

Answer (1)
$T=2\pi \sqrt{\frac{m}{F}x}$
$\frac{\Delta T}{T}\times 100=\frac{1}{2}\frac{\Delta m}{m}\times 100+\frac{1}{2}\frac{\Delta x}{x}\times 100$
$=\frac{-2\%}{2}+\frac{4\%}{2}$
$=1\%$