NEET Physics Mathematical Tools, Units & Dimensions NEET PYQ-Mathematical Tools, Units and Dimensions

  • 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                   [AIPMT(M) 2010]

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

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

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

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

    Correct Answer: B

    Solution :

    \[h=\frac{1}{2}g{{t}^{2}}\] or \[g=\frac{h}{{{t}^{2}}}\]
    \[\therefore \]      \[\log \,g=\log \,h-2\,\log \,t\]
    \[{{\left( \frac{\Delta g}{g}\times 100 \right)}_{\max }}=\left( \frac{\Delta h}{h}\times 100 \right)+2\left( \frac{\Delta t}{t}\times 100 \right)\]        \[={{e}_{1}}+2{{e}_{2}}\]


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