Density of a cube is measured by measuring its mass and length of its sides. If maximum error in mea

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1.Units, Dimensions and Measurement

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The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively, then find the maximum error in the measurement of the density of cube.......... $\%$

A

$12$

B

$14$

C

$7$

D

$9$

(AIPMT-1996)

Solution

$\rho \, = \,\frac{M}{V} = \frac{M}{{{L^3}}}$

$\Rightarrow \,\frac{{\Delta \rho }}{\rho } = \frac{{\Delta M}}{M} + \frac{{3\Delta L}}{L}$

$\Rightarrow \,\frac{{\Delta \rho }}{\rho } = 3+2\times 3=9\%$

Standard 11

Physics

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