KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • question_answer
    When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is 'a' (just after release). Then its acceleration when it has acquired two third of the maximum velocity:

    A) \[\frac{a}{3}\]

    B) \[\frac{2a}{3}\]

    C) \[\frac{a}{6}\]

    D) none of these

    Correct Answer: A

    Solution :

    When the ball is just released, the net force on ball is \[{{W}_{eff}}\,(\text{= mg}-\text{buoyant}\,\,\text{force})\]
    The terminal velocity \['{{v}_{f}}'\] of the ball is attained when net force on the ball is zero.
    \[\therefore \]      Viscous force \[6\,\pi \,\eta \,r\,{{v}_{f}}={{W}_{eff}}\]
    When the ball acquires \[\frac{2}{3}rd\] of its maximum velocity \[{{v}_{f}}\]
    the viscous force is \[=\frac{2}{3}{{W}_{eff}}.\]
    Hence net force is \[{{W}_{eff}}-\frac{2}{3}{{W}_{eff}}=\frac{1}{3}{{W}_{eff}}\]
    \[\therefore \]      required acceleration is \[=\frac{a}{3}\]

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