question_answer

Find the value of x in the relation \[Y=\frac{{{T}^{x}}.\cos \theta .\tau }{{{L}^{3}}}\], where Y is Young's modulus. T is time period, \[\tau \] is torque and L is length.

Answer:

                \[Y=\frac{{{T}^{x}}.\cos \theta .\tau }{{{L}^{3}}}\] \[{{T}^{x}}=\frac{Y{{L}^{3}}}{\cos \theta .\tau }=\frac{\left[ M{{L}^{-1}}{{T}^{-2}} \right]}{\left[ M{{L}^{2}}{{T}^{-2}} \right]}=1\]         \[\therefore \] \[x=0\]