Q 11-01-200JEE MainJEE Main 2020 (6 Sep, Shift 1)Easy
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\dfrac{x}{100}\right)\%$. If the relative errors in measuring the mass and the diameter are $6.0\%$ and $1.5\%$ respectively, the value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 1050
$\rho = \dfrac{m}{\frac\pi6 d^3}$, so
$$\frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 3\frac{\Delta d}{d} = 6.0\% + 3(1.5\%) = 10.5\%$$
$10.5 = \dfrac{x}{100} \Rightarrow x = 1050$.
Solution by Sreeraj P, M.Sc Physics