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)

zero

Answer 2

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