Durring Searle's experiment, zero of the Vernier scale lies between $3.20 \times 10^{-2} m$ and $3.25 \times 10^{-2} m$ of the main scale. The $20^{\text {th }}$ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of $2 \ kg$ is applied to the wire, the zero of the Vernier scale still lies between $3.20 \times 10^{-2} m$ and $3.25 \times 10^{-2} m$ of the main scale but now the $45^{\text {th }}$ division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is $2 m$. and its cross-sectional area is $8 \times 10^{-7} m ^2$. The least count of the Vernier scale is $1.0 \times 10^{-5} m$. The maximum percentage error in the Young's modulus of the wire is
$8$
$7$
$6$
$5$
The temperatures of two bodies measured by a thermometer are $t_{1}=20^{\circ} C \pm 0.5^{\circ} C$ and $t_{2}=50^{\circ} C \pm 0.5^{\circ} C$ Calculate the temperature difference and the error theirin.
A simple pendulum is being used to determine the value of gravitational acceleration $\mathrm{g}$ at a certain place. The length of the pendulum is $25.0\; \mathrm{cm}$ and a stop watch with $1\; \mathrm{s}$ resolution measures the time taken for $40$ oscillations to be $50\; s$. The accuracy in $g$ is ....... $\%$
A physical quantity $P$ is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$ The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$
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 $mA$ ?
A physical quantity $X$ is related to four measurable quantities $a,\, b,\, c$ and $d$ as follows $X = a^2b^3c^{\frac {5}{2}}d^{-2}$. The percentange error in the measurement of $a,\, b,\, c$ and $d$ are $1\,\%$, $2\,\%$, $3\,\%$ and $4\,\%$ respectively. What is the percentage error in quantity $X$ ? If the value of $X$ calculated on the basis of the above relation is $2.763$, to what value should you round off the result.