RAJASTHAN PMT Rajasthan - PMT Solved Paper-1998

  • question_answer
    A particle is executing S.H.M. its maximum velocity is\[{{\upsilon }_{0,}}\] then what will be its velocity at a distance half of the amplitude from mean position?

    A) \[\frac{{{\upsilon }_{0}}}{2}\]                    

    B)        \[{{\upsilon }_{0}}\]

    C) \[{{\upsilon }_{0}}\sqrt{\frac{3}{2}}\]                     

    D)        \[{{\upsilon }_{0}}\sqrt{\frac{3}{2}}\]

    Correct Answer: D

    Solution :

    \[{{\upsilon }_{\max }}=a\omega \] \[{{\upsilon }_{0}}=a\omega \] Velocity \[{{\upsilon }_{1}}=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] \[=\omega \sqrt{{{a}^{2}}-\frac{{{a}^{2}}}{4}}=\frac{\sqrt{3}}{2}a\omega =\frac{\sqrt{3}}{2}{{\upsilon }_{0}}\]


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