JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    A student performs an experiment for determination of \[g\left[ =\frac{4{{\pi }^{2}}l}{{{T}^{2}}} \right],\] where \[l=1\,m\]and he commits an error of \[\Delta \,L.\] For the experiment, he takes the time for n oscillations with the stopwatch for least count \[\Delta \,T\] and he commits a human error of 0.1 sec. For which of the following data, the measurement of g will be most accurate.
    \[\Delta \,L\] \[\Delta \,T\] n Amplitude of Oscillations
    A 5 mm 0.2s 10 5mm
    B 5 mm 0.2s 20 5 mm
    C 5 mm 0.1s 20 1 mm
    D 1 mm 0.1s 50 1 mm

    A)  A                                

    B)  B

    C)  C                                

    D)  D

    Correct Answer: D

    Solution :

    The worst case is to be considered, as human errors are random in nature. \[\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\frac{\Delta T}{n}\] Error is minimum in option [d] in which no. of reading is maximum and amplitude is small.


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