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1.Units, Dimensions and Measurement
medium
Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are
A
$[{M^{3/2}}\,{L^{ - 1/2}}\,{T^{ - 2}}]$
B
$[{M^{3/2}}\,{L^{ 1/2}}\,{T^{ 2}}]$
C
$[{M^{3/2}}\,{L^{ - 1/2}}\,{T^{2}}]$
D
$[{M^{-3/2}}\,{L^{ - 1/2}}\,{T^{ 2}}]$
Solution
$[\mathrm{B}]=[\sqrt{\mathrm{d}}]=\left[\mathrm{M}^{1 / 2} \mathrm{L}^{-3 / 2}\right]$
$\Rightarrow\left[\mathrm{M}^{1} \mathrm{L}^{1} \mathrm{T}^{-2}\right]=\frac{[\alpha]}{\left[\mathrm{M}^{1 / 2} \mathrm{L}^{-3 / 2}\right]}$
$[\alpha]=\left[M^{3 / 2} L^{-1 / 2} T^{-2}\right]$
Standard 11
Physics
