JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    A disc of mass 10 kg is kept floating horizontally by throwing 10 marbles per second against it from below. The marbles strike the disc normally and rebound downwards with the same speed. If the mass of each marble is 5 g, the velocity with which the marbles are strike the disc is \[(g=9.8\,m\,{{s}^{-2}})\]

    A)  \[0.98\,m{{s}^{-1}}\]                    

    B)  \[9.8\,\,m{{s}^{-1}}\]

    C)  \[1.96\,\,m{{s}^{-1}}\]                 

    D)  \[19.6\,\,m{{s}^{-1}}\]

    Correct Answer: A

    Solution :

     Let m be mass of each marble and \[{{m}_{d}}\] be the mass of disc change in momentum of each marble \[(a=b=c\]. Change in momentum of nt marbles \[\alpha =\beta =\gamma ={{90}^{o}}\]. Let, the disc be balanced in mid air for a time t. Then, by impulse, momentum theorem impulse = Change in momentum. \[({{m}_{d}}g)t=2mv\times nt\] \[\alpha =\beta =\gamma \ne {{90}^{o}}\]           \[{{p}_{1}}=\frac{nRT}{{{V}_{1}}}=\frac{2\times 0.0821\times 243.6}{20}=2\,\text{atm}\] \[\Delta S=nR\,\,In\,\left( \frac{{{p}_{1}}}{{{p}_{2}}} \right)\]


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