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NEET Sample Paper NEET Sample Test Paper-56

  • question_answer
    The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/min when water is being drained out at a constant rate. The amount of water drained in cc per minute is [\[{{n}_{1}}\]= refractive index of air, \[{{n}_{2}}\]= refractive index of water]

    A) \[n\frac{x\pi {{R}^{2}}{{n}_{1}}}{{{n}_{2}}}\]                     

    B) \[n\frac{x\pi {{R}^{2}}{{n}_{2}}}{{{n}_{2}}}\]

    C) \[n\frac{2\pi R{{n}_{1}}}{{{n}_{2}}}\]            

    D) \[\pi {{R}^{2}}x\]

    Correct Answer: B

    Solution :

    [b] \[\frac{real\,depth}{apparent\,depth\,}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{h}{x}\] Differentiate with respect to time \[\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{dh/dt}{dx/dt}\] Change in real depth \[=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\times change\,in\] \[\frac{dh}{dt}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}cm/mim\] Amount of water drained in CC per minute \[\frac{dh}{dt}\times \pi {{R}^{2}}=x\pi {{R}^{2}}\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\]


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