Question

Given: Force $=\frac{\alpha}{\text { density }+\beta^{3}}$ What are the dimensions of $\alpha, \beta$ ?

• A. $ML ^{-2} T ^{-2}, ML ^{-1 / 3}$
• B. $M^{2} L^{4} T^{-2}, M^{-1 / 3} L^{-1}$
• C. $M^{2} L^{-2} T^{-2}, M^{1 / 3} L^{-1}$
• D. $M^{2} L^{-2} T^{-2}, M L^{-3}$

Answer 1

Answer: (C)

$\beta^{3}=$ density $=M^{1} L^{-3}$
$\beta=M^{1 / 2} L^{-1}$
Also; $\alpha=$ force $\times$ density
$=ML T^{-2} \times M^{1} L^{-3}$
$= MLT ^{-2} \times M ^{1} L ^{-3}=\left[ M ^{2} L ^{-2} T ^{-2}\right]$