The density of a cube is measured by measurin | vedclass

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(D) The density $\rho$ of a cube is given by the formula $\rho = \frac{M}{V} = \frac{M}{l^3}$,where $M$ is the mass and $l$ is the length of the side

Vedclass · Accepted Answer

$13$

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(D) The density $ho$ of a cube is given by the formula $ho = \frac{M}{V} = \frac{M}{l^3}$,where $M$ is the mass and $l$ is the length of the side of the cube.The relative error in density is given by $\frac{\Delta ho}{ho} = \frac{\Delta M}{M} + 3 \frac{\Delta l}{l}$.To find the percentage error,we multiply by $100$:$\frac{\Delta ho}{ho} 	imes 100 = \left( \frac{\Delta M}{M} 	imes 100 ight) + 3 \left( \frac{\Delta l}{l} 	imes 100 ight)$.Given that the percentage error in mass $\frac{\Delta M}{M} 	imes 100 = 4\%$ and the percentage error in length $\frac{\Delta l}{l} 	imes 100 = 3\%$.Substituting these values:Percentage error in density $= 4\% + 3(3\%) = 4\% + 9\% = 13\%$.

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 $4\%$ and $3\%$ respectively,the maximum error in the measurement of density will be ........ $\%$

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