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]
  • A

    $13$

  • B

    $14$

  • C

    $12$

  • D

    $16$

Similar Questions

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]

In a simple pendulum experiment, the maximum percentage error in the measurement of length is $2\%$ and that in acceleration due to gravity $g$ is $4\%$. Then the maximum percentage error in determination of the time-period is

Explain least count and least count error. Write a note on least count error.

If there is an error of $1\%$ in calculation of mass of disc and $1.5\%$ error in radius, then $\%$ error in moment of inertia about an axis tangent to disc is  .......... $\%$

A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?

$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds

$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second

$(C)$ Percentage error in the determination of $g$ is $5 \%$

$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

  • [IIT 2010]