Question

Force $F$ and density $d$ are related as $F=\frac{\alpha}{\beta+\sqrt{d}}$ then find the dimensions of $\alpha$ :

• A. $\left[ M ^{1 / 2} L ^{-1 / 2} T ^{-2}\right]$
• B. $\left[ M ^{3 / 2} L ^{1 /2 \,T ^{2}}\right]$
• C. $\left[ M ^{3 / 2} L ^{-1 / 2} T ^{-2}\right]$
• D. $\left[ M ^{2} L ^{-1 / 2} T ^{2}\right]$

Answer 1

Answer: (C)

$[\alpha]=[ F ][\sqrt{ d }]$
$= MLT ^{-2}\left[ ML ^{-3}\right]^{1 / 2}$
$= M ^{3 / 2} L ^{-1 / 2} T ^{-2}$