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NEET PHYSICSMedium

A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate gg, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1e_1 and e2e_2 respectively, the percentage error in the estimation of gg is

A

e2e1e_2 - e_1

B

e1+2e2e_1 + 2e_2

C

e1+e2e_1 + e_2

D

e12e2e_1 - 2e_2

Step-by-Step Solution

From the equation of motion for a freely falling body initially at rest, the distance ss traversed in time tt is given by s=12gt2s = \frac{1}{2}gt^2. Rearranging for gg, we get g=2st2g = \frac{2s}{t^2}. The maximum percentage error in gg is the sum of the percentage error in ss and twice the percentage error in tt. Therefore, % error in g=% error in s+2×(% error in t)=e1+2e2\% \text{ error in } g = \% \text{ error in } s + 2 \times (\% \text{ error in } t) = e_1 + 2e_2.

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