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NEET Sample Paper NEET Sample Test Paper-83

  • question_answer
    Particle each of mass m are falling into weighing pan from height H at a rate of n particles per second. Find reading of weighing pan after time T, if collision of particle with weighing pan is perfectly inelastic. (Neglect oscillation of weighing pan).

    A)  \[\operatorname{mgH} + mgnT\]           

    B)  \[mn\,(gT\,+\,\,\sqrt{2\,\,gH})\]

    C)  \[\operatorname{mng}\,\sqrt{2\,gH}\]                 

    D)  None of these                                    

    Correct Answer: B

    Solution :

    Reading of weighing pan is due to two reasons = [Force due to momentum transfer to it + force due to weight] Force exerted due to momentum transfer \[\frac{dp}{dt}=\frac{d}{dt}[m\sqrt{2gH}\,\times nT]=mn\sqrt{2gH}\] Force due to weight \[=\,\,\,mg \times \,\,nT = mgn\,T\] \[\therefore \] Reading to weighing \[\operatorname{pan}=mgn\,T\,\,+\,\,mn\,\sqrt{2gH}\] \[=\,\,\,mn(gT\,\,+\,\,\sqrt{2gH})\]


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