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

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0.49 m

0.98 m

1.96 m

2.12 m

answer is C.

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Detailed Solution

From, $s = u t + \frac{1}{2} a t^{2}$

$h = 0 + \frac{1}{2} \times 9.8 {(2)}^{2} = 19.6 m$

$\frac{Δ h}{h} = \pm (\frac{Δ t}{t}) (∵ a = g = c o n s \tan t)$

$= \pm 2 (\frac{0.1}{2}) = \pm \frac{1}{10}$

$Δ h = \frac{h}{10} = \frac{19.6}{10}$

$= 1.96 m$

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