Question

The density of a cube is measured by measuring its mass and length of its sides. If the maximum errors in the measurement of its mass and length are 4% and 3% respectively, the maximum error in density is –

• A. 1%
• B. 7%
• C. 5%
• D. 13%

Answer 1

Answer: (D)

13%

Answer 2

$\mathbf{\lambda}_{\mathbf{m}}\mathbf{T = b}$or $b^{4} = \lambda_{m}^{4}T^{4}$ and $\frac{energy}{area - time} = \sigma T^{4}$

or $\sigma = \frac{energy}{(area - time)T^{4}}$

\ $\sigma b^{4} = \left( \frac{energy}{area - time} \right)\lambda_{m}^{4}$

or =$\left\lbrack \sigma b^{4} \right\rbrack\frac{\lbrack ML^{2}T^{- 2}\rbrack}{\lbrack L^{2}\rbrack\lbrack T\rbrack}\lbrack L^{4}\rbrack\ = \ \lbrack\text{M}\text{L}^{4}T^{\text{-3}}\rbrack$