Physics - Unit & Dimension Question with Solution | TestHub

$\mathrm{P}\propto {\mathrm{S}}^a{\mathrm{I}}^b{\mathrm{h}}^c$
$\left[\mathrm{M}\mathrm{L}{\mathrm{T}}^{-1}\right]={\left[\mathrm{M}{\mathrm{T}}^{-2}\right]}^a{\left[\mathrm{M}{\mathrm{L}}^2\right]}^b{\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]}^C$
$\left[\mathrm{M}\mathrm{L}{\mathrm{T}}^{-1}\right]=\left[{\mathrm{M}}^{a+b+c}{\mathrm{L}}^{2b+2c}{\mathrm{T}}^{-2a-c}\right]$
From comparing the power on both side
$a+b+c=1$
$2b+2c=1$
$-2a-c=-1$
From the above three equations we will get
$a=\frac{1}{2}, b=\frac{1}{2}\& c=0$
$\mathrm{P}\propto {\mathrm{S}}^{\frac{1}{2}}{\mathrm{I}}^{\frac{1}{2}}{\mathrm{h}}^0$