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NEET Sample Paper NEET Sample Test Paper-55

  • question_answer
    If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second then non-zero integers x, y and z such that \[{{P}^{\,x}}\,\,{{Q}^{\,y}}\,\,{{C}^{\,z}}\] is dimensionless, are-

    A) \[x=1,\text{ }y=1,\text{ }z=-1\]

    B) \[x=1,\text{ }y=-1,\text{ }z=1\]

    C) \[x=-1,\text{ }y=1,\text{ }z=1\]

    D)   \[x=1,\text{ }y=1,\text{ }z=1\]

    Correct Answer: B

    Solution :

    \[\left[ P \right]\,=\,\left[ \frac{F}{A} \right]\,=\,\left[ M{{L}^{-1}}{{T}^{-2}} \right].\,\,\left[ C \right]=\left[ L{{T}^{-1}} \right]\] \[\left[ Q \right]\,=\,\frac{\left[ E \right]}{\left[ A \right]\left[ T \right]}\,\,=\,\,\left[ M{{T}^{-3}} \right]\] Given that:  \[{{P}^{x}}\,{{Q}^{y}}\,{{C}^{z}}\,=\,\,{{M}^{0}}{{L}^{0}}{{T}^{0}}\] \[{{M}^{x+y}}\,{{L}^{-x+z}}\,\,{{T}^{-2x-z-3y}}\,\,=\,{{M}^{0}}{{L}^{0}}{{T}^{0}}\] \[\therefore \,\,\,x+y=0;\,\,-2x-z-3y=0\] Solving we get: \[x=1,\,\,y=-1,\text{ }z=1\]


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