JEE Main & Advanced Sample Paper JEE Main - Mock Test - 25

  • question_answer
    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 g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are \[{{e}_{1}}\] and \[{{e}_{2}}\] respectively, the percentage error in the estimation of g is                                                            

    A) \[{{e}_{1}}+2{{e}_{2}}\]

    B)                    \[{{e}_{1}}+{{e}_{2}}\]               

    C)   \[{{e}_{1}}-2{{e}_{2}}\]              

    D)        \[{{e}_{2}}-{{e}_{1}}\]

    Correct Answer: A

    Solution :

    [a] \[h=\frac{1}{2}g{{t}^{2}}\,\,\,\,\,\Rightarrow \,\,\,\,g=\frac{2h}{{{t}^{2}}}\] then \[\frac{\Delta g}{g}\times 100=\left( \frac{\Delta h}{h}+2\frac{\Delta t}{t} \right)\times 100={{e}_{1}}+2{{e}_{2}}\]


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