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The density of a cube is measured by measuring its mass and 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 ........ $\%$
$7$
$9$
$12$
$13$
Solution
$\,\delta = \frac{M}{V} = \frac{M}{{{l^3}}}$
Percentage error in density $ = \left[ {\frac{{\Delta M}}{M} + 3\frac{{\Delta l}}{l}} \right] \times 100\,\,\,\, = [4 + 3 \times 3] \times 100\,\,$
$\, = [4 + 9] \times 100\,\,\,\,\, = 13\% $
Similar Questions
A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.
| Physical Quantity | Least count of the Equipment used for measurement | Observed value |
| Mass $({M})$ | $1\; {g}$ | $2\; {kg}$ |
| Length of bar $(L)$ | $1\; {mm}$ | $1 \;{m}$ |
| Breadth of bar $(b)$ | $0.1\; {mm}$ | $4\; {cm}$ |
| Thickness of bar $(d)$ | $0.01\; {mm}$ | $0.4 \;{cm}$ |
| Depression $(\delta)$ | $0.01\; {mm}$ | $5 \;{mm}$ |
Then the fractional error in the measurement of ${Y}$ is
