Physics

# While measuring the time of fall of a body from a height, a person makes an error or $2\%$ in the value of acceleration due to gravity and an error of $4\%$ in the value of height. The percentage error in the measurement of time of fail is?

$3\%$

##### SOLUTION

Time period of free fall

$t=\sqrt{\dfrac{2h}{g}}$

Take log on both side and differentiate.

$\dfrac{\Delta t}{t}=\dfrac{1}{2}\left( \dfrac{\Delta h}{h}+\dfrac{\Delta g}{g} \right)=\dfrac{1}{2}\left( 0.04+0.02 \right)=0.03$

Hence, error in time is $3\,\%$

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Single Correct Medium Published on 18th 08, 2020
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