2. Sample Papers
  3. KVPY

KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    In an experiment to determine the acceleration due to gravity g, the formula used for the time Period of a periodic motion is \[T=2\pi \sqrt{\frac{7\left( R-r \right)}{5g}}\]. The values of R and r are Measured to be \[\left( 60\text{ }\pm \text{ }1 \right)\]mm and \[\left( 10\text{ }\pm \text{ }1 \right)\]mm, respectively. In five successive measurements, the time period is found to be\[0.52s,\text{ }0.56s,\text{ }0.57s,\text{ }0.54s\text{ }and\text{ }0.59s\].The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement is incorrect?

    A) The error in the measurement of r is \[~10%\]

    B) The error in the determined value of g is \[11\text{ }%\]

    C) The error in the measurement of T is \[~3.75%\]

    D) none of these

    Correct Answer: C

    Solution :

    % error in measurement of ?r?
    \[=\frac{1}{10}\times 100=10%\] \[{{T}_{\operatorname{mean}}}=\frac{0.52+0.56+0.57+0.54+0.59}{6}=0.556\approx 0.56\,\,S\]
    \[{{\Delta }_{T}}=\frac{0.04+0+0.01+0.02+0.03}{6}=0.016\approx 0.02\,S\]
    \[\therefore %\]error in the measurement of ?T? \[=\frac{0.02}{0.56}\times 100=3.57%\]
    \[%\]error in the value of \[g\]\[=2\frac{\Delta T}{T}\times 100+\left( \frac{\Delta R+\Delta r}{R-r} \right)\times 100\]\[2\left( 3.57 \right)+\left( \frac{1+1}{60-10} \right)\times 100=\approx 11%\]


You need to login to perform this action.
You will be redirected in 3 sec spinner