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VMMC VMMC Medical Solved Paper-2007

  • question_answer
    The similar magnets of magnetic moments \[{{M}_{1}}\] and \[{{M}_{2}}\] are taken and vibrate in a vibration magnetometer with their (i) like poles together (ii) unlike poles together. If the ratio of the time periods is\[\frac{1}{2}\], then the ration of \[{{M}_{1}}\]and \[{{M}_{2}}\left( ie,\frac{{{M}_{1}}}{{{M}_{2}}} \right)\]

    A) 0.5                         

    B)        2                             

    C)        \[\frac{5}{3}\]                   

    D)        \[\frac{1}{3}\]

    Correct Answer: C

    Solution :

    The time period (T) of vibration magnetometer is \[T=2\pi \sqrt{\frac{I}{MH}}\] where \[I\] is moment of inertia, M the magnetic moment and H the horizontal component of earths field. When likes poles are placed together. \[M={{M}_{1}}+{{M}_{2}}\] When unlike poles are placed together. \[M={{M}_{1}}-{{M}_{2}}\] \[\therefore \]  \[\frac{T}{T}=\sqrt{\frac{{{M}_{1}}-{{M}_{2}}}{{{M}_{1}}+{{M}_{2}}}}\] \[\Rightarrow \]               \[{{\left( \frac{T}{T} \right)}^{2}}=\frac{{{M}_{1}}-{{M}_{2}}}{{{M}_{1}}+{{M}_{2}}}\] Given, \[\frac{T}{T}=\frac{1}{2}\] \[\therefore \]  \[\frac{1}{4}=\frac{{{M}_{1}}-{{M}_{2}}}{{{M}_{1}}+{{M}_{2}}}\] \[\Rightarrow \]               \[4{{M}_{1}}-4{{M}_{2}}={{M}_{1}}+{{M}_{2}}\] \[\Rightarrow \]               \[3{{M}_{1}}=5{{M}_{2}}\] \[\Rightarrow \]               \[\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{5}{3}.\]


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