KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    In figure shown, find the magnitude of acceleration of m, given that string is inextensible and mass less and the acceleration of M is \[2\text{ }m/{{s}^{2}}\] towards left -

    A) \[2\sqrt{3}\,\,m/{{s}^{2}}\]

    B) \[3\sqrt{2}\,\,m/{{s}^{2}}\]

    C) \[4\sqrt{2}\,\,m/{{s}^{2}}\]

    D) \[2\sqrt{5}\,\,m/{{s}^{2}}\]

    Correct Answer: D

    Solution :

    Let X be the leftward displacement of m and x and y be the leftward and downward displacement of M.
    Let \[AB={{\ell }_{1}};\] \[BC={{\ell }_{2}}:\] \[CD={{\ell }_{3}}\] and \[Am={{\ell }_{4}}\]when M moves towards left, say by x, then
    \[AB=({{\ell }_{1}}-x)\]
    \[BC={{\ell }_{2}}\]
    \[CD={{\ell }_{3}}-x\]
    \[Am={{\ell }_{4}}+y\]
    Total length of string remain constant
    \[\therefore {{\ell }_{1}}-x+{{\ell }_{2}}+{{\ell }_{3}}-x+{{\ell }_{4}}+y={{\ell }_{1}}+{{\ell }_{2}}+{{\ell }_{3}}+{{\ell }_{4}}\]
    \[\therefore 2x=y\]
    Acceleration of \[M={{a}_{M}}=2m/{{s}^{2}}\]
    Double differentiating this equation
    \[{{a}_{y}}\] is downward acceleration of \[m=4m/{{s}^{2}}\]
    m is also moving in left direction along with M.
    m has acceleration in horizontal direction also horizontal acceleration of m is same as that of M i.e. \[2\,m/{{s}^{2}}\]
    \[\therefore \] Net acceleration of \[m=\sqrt{{{2}^{2}}+{{4}^{2}}}=2\sqrt{5}\]

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