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 (x/100) %. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______. Numerical answer type. Work it out, then open the answer.

Answer: 1050. ρ = (m)/(4/3π (D/2)³) = (6m)/(π D³) ⇒ (Δ ρ)/(ρ) = (Δ m)/(m) + 3(Δ D)/(D) = 6.0% + 3(1.5%) = 10.5% = (1050)/(100)% Answer: x = 1050.

The density of a solid metal sphere is determined by measuring its… | JEE Main 2020 (6 Sep, Shift 1)

Q92JEE Main 2020 · 6 SEP · SHIFT 1Medium

Errors in Measurement

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_______.

Numerical answer type. Work it out, then open the answer.

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Answer: 1050

$\rho = \frac{m}{\frac{4}{3}\pi (D/2)^3} = \frac{6m}{\pi D^3} \Rightarrow \frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + 3\frac{\Delta D}{D}$
$= 6.0\% + 3(1.5\%) = 10.5\% = \frac{1050}{100}\%$
Answer: $x = 1050$ .

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