In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density is
$0.10\,\,kg/m^3$
$0.31\,\,kg/m^3$
$0.07\,\,kg/m^3$
None of these
The relative error in the determination of the surface area of a sphere is $\alpha $. Then the relative error in the determination of its volume is
Explain least count and least count error. Write a note on least count error.
If error in measuring diameter of a circle is $4\%$, the error in circumference of the circle would be
A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is
The least count of stop watch is $\frac{1}{5}\,second$. The time of $20$ oscillations of pendulum is measured to be $25\,seconds$. Then percentage error in the measurement of time will be.......... $\%$