So we can say that expression of T should be in this form T = (Some Number ) $(m)^{a} (l)^{b} (g)^{c}$
Find the values of a,b, and c

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Solution

$T \propto m^{a} l^{b} g^{c} M^{0} L^{0} T^{1} = M^{a} L^{b} . L^{c} T^{- 2 b} M^{0} L^{0} T^{1} = M^{a} L^{b + c} T^{- 2 b}$

By comparing,
$a = 0 - 2 b = 1 b = - \frac{1}{2} b + c = 0 c = \frac{1}{2} a = 0, b = \frac{1}{2}, c = \frac{1}{2}$

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So we can say that expression of T should be in this form T = (Some Number ) (m)a( l)b(g)cFind the values of a,b, and c

T∝malbgcM0L0T1=MaLb.LcT−2bM0L0T1=MaLb+cT−2bBy comparing,a=0−2b=1b=−12b+c=0c=12a=0,b=12,c=12

So we can say that expression of T should be in this form T = (Some Number ) $(m)^{a} (l)^{b} (g)^{c}$
Find the values of a,b, and c

$T \propto m^{a} l^{b} g^{c} M^{0} L^{0} T^{1} = M^{a} L^{b} . L^{c} T^{- 2 b} M^{0} L^{0} T^{1} = M^{a} L^{b + c} T^{- 2 b}$

By comparing,
$a = 0 - 2 b = 1 b = - \frac{1}{2} b + c = 0 c = \frac{1}{2} a = 0, b = \frac{1}{2}, c = \frac{1}{2}$