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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Critical Thinking

  • question_answer
    A stone tied to a string of length \[L\] is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \[u\]. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is    [IIT 1998; CBSE PMT 2004]

    A)             \[\sqrt{{{u}^{2}}-2gL}\]

    B)               \[\sqrt{2gL}\]

    C)             \[\sqrt{{{u}^{2}}-gl}\]

    D)               \[\sqrt{2({{u}^{2}}-gL)}\]

    Correct Answer: D

    Solution :

                    \[\frac{1}{2}m{{u}^{2}}-\frac{1}{2}m{{v}^{2}}=mgL\]             Þ \[v=\sqrt{{{u}^{2}}-2gL}\]             \[|\vec{v}-\vec{u}|\,=\sqrt{{{u}^{2}}+{{v}^{2}}}=\sqrt{{{u}^{2}}+{{u}^{2}}-2gL}=\sqrt{2({{u}^{2}}-gL)}\]


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