JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Morning)

  • question_answer
    A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 \[N{{m}^{-1}}\](see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillation it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance \[10\Omega \]and air drag negligible, N will be close to :                                                   [JEE Main 8-4-2019 Morning]

    A) 50000             

    B) 5000

    C) 10000             

    D) 1000

    Correct Answer: B

    Solution :

    \[{{T}_{0}}=2\pi \sqrt{\frac{m}{k}}\]         \[=\frac{2\pi }{\sqrt{10}}\]             \[A={{A}_{0}}{{e}^{-t/\gamma }}\]             \[\therefore \]for\[A=\frac{{{A}_{0}}}{e},t=\gamma \]             \[t=\gamma =\frac{2m}{b}=\frac{2m}{\frac{{{B}^{2}}{{\ell }^{2}}}{R}}={{10}^{4}}s\] \[\therefore \] No of oscillation\[\frac{t}{{{T}_{0}}}=\frac{{{10}^{4}}}{2\pi /\sqrt{10}}\approx 5000\].


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