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Haryana PMT Haryana PMT Solved Paper-2011

  • question_answer
    A particle moves is X-Y plane under the                 influence of a force F such that its            instantaneous    momentum       is \[\mathbf{p}=\mathbf{i}2\cos t~+\mathbf{j}2\sin t,\] what is the angle between the force    and instantaneous momentum?

    A)                 \[0{}^\circ \]                                      

    B)  \[180{}^\circ \]

    C)                 \[90{}^\circ \]                                   

    D) \[45{}^\circ \]

    Correct Answer: C

    Solution :

                    Here, p = i2 cost +j2 cost t                 \[F\frac{dp}{dt}=-2i\sin t+2j\]cos t                 \[F.P=(-2i\sin t+2j\cos t).(2i\cos t+j\sin t)\]                 \[=-4\sin t\cos t=+\,4\sin t\cos t=0\]                 Therefore, \[\theta ={{90}^{0}}\]


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