(C) The height $h$ of the bridge is given by the equation of motion: $h = \frac{1}{2}gt^2$.Given $g = 9.8\;m/s^2$ and $t = 2\;s$,the height is $h = \f

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(C) The height $h$ of the bridge is given by the equation of motion: $h = \frac{1}{2}gt^2$.Given $g = 9.8\;m/s^2$ and $t = 2\;s$,the height is $h = \frac{1}{2} \times 9.8 \times (2)^2 = 19.6\;m$.To find the error in height $\Delta h$,we differentiate the equation $h = \frac{1}{2}gt^2$ with respect to $t$:$dh = gt \cdot dt$.Substituting the given values,where $dt = \Delta t = 0.1\;s$:$\Delta h = 9.8 \times 2 \times 0.1 = 1.96\;m$.Thus,the error in the estimation of the height is $1.96\;m$.

Class 11 Physics Units, Dimensions and Measurement Errors of Measurement

Medium

In an experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the measurement of time is $0.1\;s$ at the end of $2\;s$,then the error in the estimation of the height of the bridge will be (in $;m$)

A
$0.49$
B
$0.98$
C
$1.96$
D
$2.12$

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Units, Dimensions and Measurement

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Errors of Measurement

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:

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If $P = \frac{A^3}{B^{5/2}}$ and $\Delta A$ is the absolute error in $A$ and $\Delta B$ is the absolute error in $B$,then the absolute error $\Delta P$ in $P$ is:

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$A$ student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90\;s$,$91\;s$,$95\;s$,and $92\;s$. If the minimum division in the measuring clock is $1\;s$,then the reported mean time should be

MediumJEE MAIN 2016

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$A$ force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$,what is the maximum percentage error in pressure (in $\%$)?

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$A$ capacitor of capacitance $(4.0 \pm 0.2) \mu F$ is charged to a potential of $(10.0 \pm 0.1) V$. The charge on the capacitor is

EasyTS EAMCET 2024

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In an experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the measurement of time is $0.1\;s$ at the end of $2\;s$,then the error in the estimation of the height of the bridge will be (in $;m$)

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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:

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