JEE PYQ: Mathematics In Physics Question 13
Question 13 - 2020 (06 Sep Shift 1)
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 $\left(\frac{x}{100}\right)$%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of $x$ is _____.
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Answer: (1050)
Solution
Density, $\rho = \frac{M}{V} = \frac{M}{\frac{4}{3}\pi\left(\frac{D}{2}\right)^3} \Rightarrow \rho = \frac{6}{\pi}MD^{-3}$ $\therefore %\left(\frac{\Delta\rho}{\rho}\right) = \frac{\Delta m}{m} + 3\left(\frac{\Delta D}{D}\right) = 6 + 3 \times 1.5 = 10.5%$ $%\frac{\Delta\rho}{\rho} = \frac{1050}{100}% = \left(\frac{x}{100}\right)%$ $\therefore x = 1050.00$
BETA
