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NEET Sample Paper NEET Sample Test Paper-66

  • question_answer
    In dimension of critical velocity \[{{\nu }_{c}}\], of liquid following through a tube are expressed as \[({{\eta }^{x}}\,{{\rho }^{y}}\,{{r}^{z}})\], where \[\eta ,\,\,\rho \,\,and\,\,r\] are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:

    A) \[1,\,\,1,\,\,1\]                

    B) \[1,\,\,-1,\,\,-1\]

    C) \[-1,\,\,-1,\text{ }1\]       

    D) \[-1,\,\,-1,\,\,-1\]

    Correct Answer: B

    Solution :

    \[{{V}_{c}}\,\propto \,\,\left[ {{\eta }^{x}}{{\rho }^{v}}{{r}^{z}} \right]\] \[\left[ {{L}^{1}}{{T}^{-1}} \right]\,\,\propto \,\,{{\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-1}} \right]}^{x}}\,{{\left[ {{M}^{1}}{{L}^{-3}} \right]}^{y}}\,{{\left[ {{L}^{1}} \right]}^{z}}\] \[\left[ {{L}^{1}}{{T}^{-1}} \right]\,\,\propto \,\,{{\left[ {{M}^{x+y}}\, \right]}^{x}}\,\left[ {{L}^{-x-3y+z}} \right]\,\left[ {{T}^{-x}} \right]\] taking comparison on both sides, \[x+y= 0,\,\,-x- 3y+z=1,\,\,-x=-1\] \[\Rightarrow \,\,x=1,\,\,y=-1,\,\,z=-1\,\,\]


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