$A$ physical quantity $X$ is given by $X = \frac{2k^3l^2}{m\sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$

  • A
    $8$
  • B
    $10$
  • C
    $12$
  • D
    $14$

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$A$ student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L^{3}}{4 b d^{3} \delta}$. The value of $g$ is taken to be $9.8 \, m/s^2$, without any significant error. His observations are as follows:
Physical QuantityLeast count and Observed value
Mass $(M)$$1 \, g$ and $2 \, kg$
Length of bar $(L)$$1 \, mm$ and $1 \, m$
Breadth of bar $(b)$$0.1 \, mm$ and $4 \, cm$
Thickness of bar $(d)$$0.01 \, mm$ and $0.4 \, cm$
Depression $(\delta)$$0.01 \, mm$ and $5 \, mm$

Then the fractional error in the measurement of $Y$ is:

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

Consider a series of measurements of the length of a box in an experiment. The readings are $2.4 \ m, 2.5 \ m, 2.6 \ m, 2.8 \ m, 3.0 \ m$. What would be the relative error?

Out of absolute error,relative error,and fractional error,which has a unit and which has no unit?

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$A$ physical quantity $P$ is given by $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. The quantity which brings in the maximum percentage error in $P$ is

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