In a experiment to measure the height of a bridge by dropping a s… - Vidyadip

MCQ

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

A
$0.49$
B
$0.98$
✓
$1.96$
D
$2.12$

✓

Answer

Correct option: C.

$1.96$

c
$s = {v_o}t + \frac{1}{2}a{t^2}$

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

$\frac{{\Delta h}}{h} = \pm 2\left( {\frac{{\Delta t}}{t}} \right)$ $(\because {a = g}$ constant$)$

$ = \pm 2\left( {\frac{{0.1}}{2}} \right) = \pm 0.1\,$

$\therefore \Delta h= \pm \frac{h}{{10}} = \pm \frac{{19.6}}{{10}}= \pm 1.96\,m$

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