If the error in measuring the diameter of a circle is $4\%$,the error in the circumference of the circle would be (in $\%$)

  • A
    $2$
  • B
    $8$
  • C
    $4$
  • D
    $1$

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In an experiment,the values of refractive indices of glass were found to be $1.54, 1.53, 1.44, 1.54, 1.56$ and $1.45$ in successive measurements. The mean absolute error is:

$A$ student measures time for $20$ oscillations of a simple pendulum as $30 \ s, 32 \ s, 35 \ s$ and $35 \ s$. If the minimum division in the measuring clock is $1 \ s$,then the correct mean time (in seconds) is:

Error in volume of a sphere is $6\%$. Error in its radius will be .......... $\%$

What is the percentage error in the measurement of the time period of a pendulum if the maximum errors in the measurement of $l$ and $g$ are $2\%$ and $4\%$ respectively?

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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:

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