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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2005

  • question_answer
    A uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by a force F. The tension in the rope at a distance I from this end is

    A)  F                                            

    B)  \[\frac{l}{L}F\]

    C) \[\frac{L}{l}F\]                                  

    D) \[\left( 1-\frac{l}{L} \right)F\]

    Correct Answer: D

    Solution :

    Suppose m be the mass of the rope per unit length. Therefore, total mass> of length \[L=mL\] \[\therefore \] Force applied  \[F=(mL)a\] or            \[a=\frac{F}{mL}\] So, tension in the rope at a distance \[l\] = Force on the length \[(L-0)\]                 or            \[T=m(L-l)a=m(1-l)\frac{F}{mL}\]                 or            \[T=\left( 1-\frac{l}{L} \right)F\]


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