Question

The speed of sound in a gas is given by
$v=\sqrt{\frac{\gamma R T}{M}} $
where the letters have usual meanings. The dimensional formula of $\gamma$ is

• A. $\left[ M ^{0} L ^{0} T ^{0}\right]$
• B. $ [MLT] $
• C. $\left[ MLT ^{-2}\right]$
• D. $\left[ M ^{0} L ^{0} T ^{-1}\right]$

Answer 1

Answer: (A)

$ v=\sqrt{\frac{\gamma R T}{M}}$
$[\gamma]=\frac{v^{2} \times M}{R \times T}=\frac{\left[ L ^{2} T ^{-2}\right][ M ]}{\left[ ML ^{2} T ^{-2} K ^{-1}\right] \times[ K ]}= M ^{0} L ^{0} T ^{0}$