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JEE Main & Advanced Physics Ray Optics Question Bank Self Evaluation Test - Ray Optics and Optical Instruments

  • question_answer
    A point object is located at a distance 15cm. from the pole of a concave mirror of focal length 10cm on its principal axis is moving with a velocity \[(8\hat{i}+11\hat{j})\]cm/s and velocity of mirror is \[(4\hat{i}+2\hat{j})\] cm/s as shown. If \[\vec{v}\] is the velocity of image. Then find the value of \[\left| {\vec{v}} \right|\] in (cm/s).

    A) 20

    B) 30    

    C) 10

    D) 40

    Correct Answer: A

    Solution :

    [a] \[{{\vec{v}}_{obj,moier}}=4\hat{i}+9\hat{j}\]\[\frac{dx}{dt}=4,\frac{dy}{dt}=9,u=-x\] \[-\frac{1}{10}=\frac{1}{V}+\frac{1}{-x};V=\frac{-10x}{x-10}\] \[{{v}_{ix}}=\frac{dV}{dt}={{\left( \frac{10}{x-10} \right)}^{2}}\left( \frac{dx}{dt} \right);{{v}_{ix}}=-16\]\[m=-\frac{V}{-x}=\frac{-10}{x-10}=\frac{y_{1}^{0}}{y}\] \[{{v}_{iy}}=-\left( \frac{10}{x-10} \right)\frac{dy}{dt};{{v}_{iy}}=-18\] \[{{\vec{v}}_{image,mirror}}=-16\hat{i}-18\hat{j};{{\vec{v}}_{image}}=-12\hat{i}-16\hat{j}\] \[|v|=20cm/s\]


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