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9th Class Science Force and laws of motion Question Bank Force and Laws of Motion

  • question_answer
    A disc of mass 10 g 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 striking the disc is\[(g=9.8\,m/{{s}^{2}})\].

    A)  0.98 m/s  

    B)  9.8 m/s

    C)  1.96 m/s

    D)  19.6 m/s

    Correct Answer: A

    Solution :

     The disc is balanced against its weight by the force which the marbles exert on the disc in upwards direction. Let us derive expression of force exerted by the marbles. Initial momentum with which a marble strikes the disc\[=mu\] Final momentum of the marble after the collision\[=-mu\] Change in momentum of one marble during collision\[=-2mu\] Momentum imparted to the disc in collision by one marble\[=2mu\] Now, force exerted is equal to rate of change of momentum. So we must multiply the momentum exerted by one marble with the number of marbles striking the disc in one second. If \[n\] be the number of marbles striking the disc in one second, then force exerted by the marbles on the disc\[=2mnu\] Now, for the equilibrium of the disc,\[2mnu=Mg\]where \[M\] is the mass of the disc. On solving, we get                \[u=0\cdot 98\,\,m/s\]


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