JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Oscillations

  • question_answer
    Two springs, each of spring constant\[k=100N/m\], are attached to a block of mass 2 kg as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass 5kg. If the block is displaced by x cm. and released, the period of oscillation in seconds is

    A) \[T=2\pi \sqrt{\frac{1}{20}}\]

    B) \[T=2\pi \sqrt{\frac{7}{1000}}\]

    C) \[T=2\pi \sqrt{\frac{1}{140}}\]

    D) \[T=2\pi \frac{49}{100}\]

    Correct Answer: C

    Solution :

    [c] \[T=2\pi \sqrt{\frac{\mu }{2k}}\]         \[\therefore \,\,\mu =\frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[T=2\pi \sqrt{\frac{10}{7\times 200}}=\frac{2\times 5}{7}=\frac{10}{7}=2\pi \sqrt{\frac{1}{140}}\]


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