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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        A plank of mass 12 kg is supported by two identical springs as shown in figure. The plank     always remains horizontal. When the plank is pressed down and released, it performs SHM with time period 3 s. When a block of mass m is attached to plank the time period changes to 6 s. The mass of the block is

    A)  48 kg                                    

    B)  36 kg

    C)  24kg                                     

    D)  12kg

    Correct Answer: B

    Solution :

                    Let spring constant of each spring be k, then the equivalent spring constant of two spring system is parallel is\[2k\]. Without mass, time period                 \[T=3s=2\pi \sqrt{\frac{12}{2k}}\] with mass, \[T=6s=2\pi \sqrt{\frac{12+m}{2k}}\] \[\frac{T}{T}=\frac{1}{2}=\sqrt{\frac{12}{12+m}}\] \[\Rightarrow \]               \[m=36kg\]


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