A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$

If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ........... $\%$

  • [JEE MAIN 2017]
  • A

    $8$

  • B

    $12$

  • C

    $32$

  • D

    $25$

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The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be   ........ $\%$

  • [AIIMS 2013]

A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$

  • [JEE MAIN 2020]

Write a note on combination of error.

The mass and volume of a body are found to be $(5.00 ± 0.05)\,kg$ and $(1.00 ± 0.05)\,m^3$ respectively. Then the maximum possible percentage error in its density is .......... $\%$

The distance $s$ travelled by a particle in time $t$ is $s=u t-\frac{1}{2} \,g t^{2}$. The initial velocity of the particle was measured to be $u=1.11 \pm 0.01 \,m / s$ and the time interval of the experiment was $t=1.01 \pm 0.1 \,s$. The acceleration was taken to be $g=9.8 \pm 0.1 \,m / s ^{2}$. With these measurements, the student estimates the total distance travelled. How should the student report the result?

  • [KVPY 2017]