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
$(2.0 \pm 0.3) \times 10^{11} \mathrm{~N} / \mathrm{m}^2$
$(2.0 \pm 0.2) \times 10^{11} \mathrm{~N} / \mathrm{m}^2$
$(2.0 \pm 0.1) \times 10^{11} \mathrm{~N} / \mathrm{m}^2$
$(2.0 \pm 0.05) \times 10^{11} \mathrm{~N} / \mathrm{m}^2$
Error in the measurement of radius of a sphere is $1\%$. The error in the calculated value of its volume is ......... $\%$
We can reduce random errors by
The current voltage relation of diode is given by $I=(e^{1000V/T} -1)\;mA$, where the applied voltage $V$ is in volts and the temperature $T$ is in degree Kelvin. If a student makes an error measuring $ \mp 0.01\;V$ while measuring the current of $5\; mA$ at $300\; K$, what will be the error in the value of current in $mA$ ?
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
Thickness of a pencil measured by using a screw gauge (least count $0.001 \,cm$ ) comes out to be $0.802 \,cm$. The percentage error in the measurement is ........... $\%$