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NEET Sample Paper NEET Sample Test Paper-82

  • question_answer
    A block of mass m, attached to a spring of spring constant k, oscillates on a smooth horizontal table. The other end of a spring is fixed to a wall. The block has a speed v, when the spring is at its natural length. Before coming to an instantaneous rest if the block moves a distance x from the mean position, then

    A)  \[x=\frac{1}{v}\,\sqrt{\frac{m}{k}}\]                

    B)  \[x=\,\sqrt{\frac{m}{k}}\]

    C)  \[x=\,V\,\sqrt{\frac{m}{k}}\]                

    D)  \[x=\,\,\sqrt{\frac{mv}{k}}\]

    Correct Answer: C

    Solution :

    Time period \[T=2\pi \sqrt{\frac{m}{k}}\]and\[\omega =\frac{2\pi }{T}=\sqrt{\frac{k}{m}}\] When spring is at its natural length, the velocity of block is maximum. So, \[v=r\omega \] According to question \[\operatorname{r}\,\,=\,\,x,\,\,So\,\,v=x\omega \] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,x=\frac{v}{\omega }=v\sqrt{\frac{m}{k}}\]


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