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VIT Engineering VIT Engineering Solved Paper-2009

  • question_answer
    Two bar magnets A and Bare placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of A and B are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]are the magnetic moments of A and B and if \[{{\text{M}}_{\text{A}}}\text{}{{\text{M}}_{\text{B}}}\], the ratio of \[{{\text{M}}_{\text{A}}}\] and \[{{\text{M}}_{\text{B}}}\]is

    A)  4 : 3           

    B)  25 : 7

    C)  7 : 5            

    D)  25 : 16  

    Correct Answer: B

    Solution :

    Ratio of magnetic moments of two magnets of equal size when in sum and difference position is \[\frac{{{M}_{A}}}{{{M}_{B}}}=\frac{T_{d}^{2}+T_{s}^{2}}{T_{d}^{2}-T_{s}^{2}}=\frac{v_{s}^{2}+v_{d}^{2}}{v_{s}^{2}-v_{d}^{2}}\] \[\frac{={{\left( \frac{1}{20} \right)}^{2}}+{{\left( \frac{1}{15} \right)}^{2}}}{{{\left( \frac{1}{15} \right)}^{2}}-{{\left( \frac{1}{20} \right)}^{2}}}\] \[=\frac{400+225}{400-225}\] \[=\frac{625}{175}=\frac{25}{7}\] \[\Rightarrow \] \[{{M}_{A}}:{{M}_{B}}=25:7\]


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