Q76 / 90 · JEE Main 2018 (08 Apr) · Physics

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are $1.5 %$ and $1 %$ , respectively, the maximum error in determining the density is:

A
$6 %$
B
$2.5 %$
C
$3.5 %$
Correct answer
D
$4.5 %$

Solution

ρ = \frac{M}{L^{3}}

\Rightarrow \frac{Δ ρ}{ρ} = \frac{Δ M}{M} + \frac{3 Δ L}{L}

\Rightarrow \frac{Δ ρ}{ρ} \times 100 = 1.5 + 3 \times 1

%

relative error,

= 4.5 %

Hence, the correct answer is option: 'D'.

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