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NEET Sample Paper NEET Sample Test Paper-23

  • question_answer
    A ball of mass m moving with velocity\[\upsilon \] strikes the bob of a pendulum at rest. The mass of the bob is also m. If the collision is perfectly inelastic, the height to which the bob will rise is given by:

    A) \[\frac{{{U}^{2}}}{8g}\]                           

    B) \[\frac{{{U}^{2}}}{4g}\]

    C) \[\frac{{{U}^{2}}}{2g}\]                           

    D) \[\frac{{{U}^{2}}}{g}\]   

    Correct Answer: A

    Solution :

    Because the collision is perfectly inelastic, hence, the two blocks stick together. By conservation of linear momentum, 2 mV = mu or \[V=u/2,\]where V is the speed of the system after collision. By conservation of energy \[2mgh=\frac{1}{2}2m{{V}^{2}}\Rightarrow gh=\frac{1}{2}{{V}^{2}}\Rightarrow gh=\frac{1}{2}{{\left( \frac{u}{2} \right)}^{2}}\] \[\Rightarrow \,\,h=\frac{{{u}^{2}}}{8g}\] Hence, the correction option is [a].


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