The errors in the measurement of mass and length of the cube is $1.5 \%$ and $2 \cdot 5 \%$ respectively.…

The errors in the measurement of mass and length of the cube is $1.5 \%$ and $2 \cdot 5 \%$ respectively. The percentage error in the measurement of density of a cube is
  1. $3 \%$
  2. $1.5 \%$
  3. $6 \%$
  4. $9 \%$

Solution

Density $p=\frac{m}{v}=\frac{m}{l^{3}}$ $\begin{aligned} \max \% \text{ error}=\frac{\Delta P}{P} \times 100 &=\frac{\Delta m}{m} \times 100+3 \times \frac{\Delta l}{l} \times 100 \\ &=(1.5+3 \times 2.5) \% \\ &=(1.5+7.5) \%=9 \% \end{aligned}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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