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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    A constant tangent force F acts at the top of a solid cylinder of mass m and radius R so that the cylinder rolls on a horizontal surface without slipping. Find the magnitude and the direction of the friction force exerted by the cylinder on the surface.  
     
     

    A) \[\frac{F}{3}\] rightward

    B) \[\frac{F}{3}\]leftward         

    C) \[\frac{2F}{3}\]rightward     

    D) \[\frac{2F}{3}\]leftward

    Correct Answer: B

    Solution :

    [b] Newton's second law is in the horizontal direction, \[F+{{f}_{F}}=m{{a}_{G}}\]                                       ... (1) For angular acceleration a, \[FR-{{F}_{f}}R={{l}_{G}}\alpha \] \[\therefore \,\,\,\,\,\,\,F-{{F}_{1}}=\frac{mR\alpha }{2}=\frac{m{{a}_{G}}}{2}\]            ? (2) Solving for \[{{F}_{f}}\] from equation (1) and (2), \[{{F}_{f}}=\frac{F}{3}\,\,\,\,\,\,\therefore \,\,\,{{F}_{f}}=\frac{F}{3}\] rightward \[\therefore \]  The force of friction exerted on the surface \[=\frac{F}{3}\]leftward


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