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NEET NEET SOLVED PAPER 2016 Phase-II

  • question_answer
    A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is

    A)  \[\frac{3}{4}\]                         

    B)  \[\frac{4}{3}\]

    C)  \[\frac{16}{9}\]                        

    D)  \[\frac{9}{16}\]

    Correct Answer: D

    Solution :

                \[{{T}_{1}}=3=\sqrt[2\pi ]{\frac{m}{k}}\]             Then, \[{{T}_{2}}=5=\sqrt[2\pi ]{\frac{m+1}{k}}\]             Dividing, \[\frac{3}{5}=\sqrt{\frac{m}{m+1}}\]             \[\frac{9}{25}=\frac{m}{m+1}\]             \[9m+9=25m\]             16m=9             \[m=\frac{9}{16}\]


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