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JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Mock Test - Units Dimenstions and Measurment

  • question_answer
    While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation \[g=4\pi _{{}}^{2}(l/T_{{}}^{2})\] will be

    A) 2%                   

    B) 4%    

    C) 7%       

    D) 10%

    Correct Answer: C

    Solution :

    [c] Given that \[\frac{\Delta l}{l}\times\] 100=+1%and \[\frac{\Delta T}{T}\times\] 100=-3% Percentage error in the measurement of g is \[\left[ \frac{4{{\pi }^{2}}l}{{{T}^{2}}} \right]=100\times \frac{\Delta l}{l}-2\times \frac{\Delta T}{T}\times 100\] =1%-2[-3%]=+7%        


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