In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $w$ is calculated as follows $w\, = \,\frac{{{a^4}{b^3}}}{{{c^2}\sqrt D }}$  error in the measurement of $w$ is .......... $\%$

  • A

    $10$

  • B

    $16$

  • C

    $18$

  • D

    $12$

Similar Questions

Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.

They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.

Least count for length $=0.1 \mathrm{~cm}$

Least count for time $=0.1 \mathrm{~s}$

Student Length of the pendulum $(cm)$ Number of oscillations $(n)$ Total time for $(n)$ oscillations $(s)$ Time period $(s)$
$I.$ $64.0$ $8$ $128.0$ $16.0$
$II.$ $64.0$ $4$ $64.0$ $16.0$
$III.$ $20.0$ $4$ $36.0$ $9.0$

If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,

  • [IIT 2008]

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed  ......... $\%$

  • [AIPMT 1995]

Explain Absolute Error, Relative Error and Percentage Error.

A physical quantity $A$ is related to four observable $a,b,c$ and $d$ as follows, $A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$, the percentage errors of measurement in $a,b,c$ and $d$ are $1\%,3\%,2\% $ and $2\% $ respectively. What is the percentage error in the quantity $A$ ......... $\%$

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 $.......\%$

  • [JEE MAIN 2023]