The speed of sound in a gas is given by v=√(γ R T/M) where the letters have usual meanings. The dimensional formula of γ is

Question

The speed of sound in a gas is given by v=√(&gamma; R T/M) where the letters have usual meanings. The dimensional formula of &gamma; is (A) [ M 0 L 0 T 0] (B)  [MLT]  (C) [ MLT -2] (D) [ M 0 L 0 T -1]

Tardigrade Admin · Accepted Answer

v=√(&gamma; R T/M) [&gamma;]=(v2 × M/R × T)=([ L 2 T -2][ M ]/[ ML 2 T -2 K -1] ×[ K ])= M 0 L 0 T 0

Q. The speed of sound in a gas is given by
$v = \frac{γ RT}{M}$
where the letters have usual meanings. The dimensional formula of $γ$ is

$[M^{0} L^{0} T^{0}]$

$[M L T]$

$[M L T^{- 2}]$

$[M^{0} L^{0} T^{- 1}]$

$v = \frac{γ RT}{M}$
$[γ] = \frac{v ^{2} \times M}{R \times T} = \frac{[ L ^{2} T ^{- 2} ] [ M ]}{[ M L ^{2} T ^{- 2} K ^{- 1} ] \times [ K ]} = M^{0} L^{0} T^{0}$

Q. The speed of sound in a gas is given by v=MγRT​​ where the letters have usual meanings. The dimensional formula of γ is

[M0L0T0]

[MLT]

[MLT−2]

[M0L0T−1]