JEE Main & Advanced Physics Work, Energy, Power & Collision Question Bank Work Done by Variable Force

  • question_answer A particle moves under the effect of a force \[F~=Cx\]from x = 0 to \[x={{x}_{1}}\]. The work done in the process is                         [CPMT 1982; DCE 2002;Orissa JEE 2005]

    A)             \[Cx_{1}^{2}\]

    B)             \[\frac{1}{2}Cx_{1}^{2}\]

    C)             \[C{{x}_{1}}\]          

    D)             Zero

    Correct Answer: B

    Solution :

                    \[W\int\limits_{0}^{{{x}_{1}}}{F.dx}=\int\limits_{0}^{{{x}_{1}}}{Cx\ dx}=C\left[ \frac{{{x}^{2}}}{2} \right]_{0}^{{{x}_{1}}}=\frac{1}{2}Cx_{1}^{2}\]

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