The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$, the percentage error in calculated volume of cylinder is ............. $\%$

  • A

    $2.1$

  • B

    $3$

  • C

    $2.01$

  • D

    $3.2$

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A physical quantity is $A = P^2/Q^3.$ The percentage error in measurement of $P$ and $Q$ is $x$ and $y$ respectively. Maximum error in measurement of $A$ is

The length of a cylinder is measured with a meter rod having least count $0.1\, cm$. Its diameter is measured with vernier calipers having least count $0.01\, cm$. Given that length is $5.0 \,cm$. and radius is $2.0 \,cm$. The percentage error in the calculated value of the volume will be ......... $\%$

In order to determine the Young's Modulus of a wire of radius $0.2\, cm$ (measured using a scale of least count $=0.001\, cm )$ and length $1 \,m$ (measured using a scale of least count $=1\, mm$ ), a weight of mass $1\, kg$ (measured using a scale of least count $=1 \,g$ ) was hanged to get the elongation of $0.5\, cm$ (measured using a scale of least count $0.001\, cm$ ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)

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Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No. Length of pendulum $(cm)$ No. of oscillations $(n)$ Total time for oscillations Time period $(s)$
$1.$ $64.0$ $8$ $128.0$ $16.0$
$2.$ $64.0$ $4$ $64.0$ $16.0$
$3.$ $20.0$ $4$ $36.0$ $9.0$

(Least count of length $=0.1 \,{m}$, least count for time $=0.1\, {s}$ )

If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $'g'$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no. ....... .

  • [JEE MAIN 2021]

The percentage error in the measurement of $g$ is $.....\%$ (Given that $g =\frac{4 \pi^2 L }{ T ^2}, L =(10 \pm 0.1)\,cm$, $T =(100 \pm 1)\,s )$

  • [NEET 2022]