Question

Show dimensionmally that the expression , T = (MgL)/(pi r^(2) is dimensiomally current , where T is Young 's modulas of the length of the wire ,Mg is the weight applied in the wire and L is the increase in the length of the wire .

Answer 1

Dimension of Young's modulus is given by ,

M(L^-1)(T^-2)

•) Now we have ,

Y = (MgL) / πr^2

Where , Y is the Young's modulus, M is the mass , L is the length and r is the radius.

•) Now taking R.H.S, we know dimensions of

Mg = ML(T^-2) , L = L , r^2 = L^2

Hence , in R.H.S we have ,

(MgL) / πr^2 = MLT^-2 * L / L^2

= MT^-2

•) Hence, the equation is dimensionally incorrect as dimenstion of Young's modulus is

M(L^-1)(T^-2)

L.H.S ≠ R.H.S