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A wire has a mass $0.3 \pm 0.003\,g$, radius $0.5 \pm 0.005\,mm$ and length $6 \pm 0.06\,cm$. The maximum percentage error in the measurement of its density is .......... $\%$
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3\%$ each, then error in the value of resistance of the wire is ........ $\%$
A vernier callipers used by student has $20$ divisions in $1\;cm$ on main scale. $10$ vernier divisions coincide with $9$ main scale divisions. When jaws are closed, zero of main scale is on left of zero of vernier scale and $6\ th$ division of vernier scale coincides with any of main scale divisions. He places a wooden cylinder in between the jaws and measures the length. The zero of vernier scale is on right of $3.20\;cm$ and $8\ th$ vernier division coincides with any main scale division. When he measures thickness of cylinder he finds that zero of vernier scale lies on right of $1.50\;cm$ mark of main scale and $6\ th$ division of vernier scale coincides with any main scale division. The correct values of measured length and diameter are respectively
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is ........ $\%$