Question

A hypothetical experiment conducted to determine Youngs formula $ Y=\frac{\cos \theta {{T}^{x}}.\tau }{{{l}^{3}}} $ .
If Y = Youngs modulus, T = time period,
t = Torque and $ l= $ length, then find the value of $ x $ .

• A. zero
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

$ y=\frac{\cos \theta {{T}^{x}}.\tau }{{{l}^{3}}} $
$ [y]=[M{{L}^{-1}}{{T}^{-2}}][T]=[{{T}^{2}}] $
$ [T]=[M{{L}^{2}}{{T}^{-2}}] $
$ \theta = $ dimensionless $ (l)=[L] $
$ [M{{L}^{-1}}{{T}^{-2}}]=\frac{{{[T]}^{x}}[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{3}}]} $
comparing the power,
$ -2+x=-2 $ $ x=0 $