Q 11-01-099JEE MainJEE Main 2024 (6 Apr, Shift 1)Easy
To find the spring constant ($k$) of a spring experimentally, a student commits a $2\%$ positive error in the measurement of time and a $1\%$ negative error in the measurement of mass. The percentage error in determining the value of $k$ is
Answer: (A) $5\%$
$T = 2\pi\sqrt{\dfrac mk} \Rightarrow k = \dfrac{4\pi^2m}{T^2}$, so
$$\frac{\Delta k}{k} = \frac{\Delta m}{m} - 2\frac{\Delta T}{T} = (-1\%) - 2(+2\%) = -5\%$$
The error in $k$ is $5\%$ (a negative error).
Solution by Sreeraj P, M.Sc Physics