Question

In [ P + a/V²] (V - b) = RT equation, the dimensional formula of a/b will be .............. where P = Pressure, V = Volume and T is temperature.
The equation of stationary wave is y = 2Asin Kx cos wt (in metre). Where A and x are in metre. w is angular frequency. Dimensions of A/k are
(A) M¹L²Tâ»Â²
(B) M¹L²Tâ»Â²K¹
(C) M¹Lâ»Â²T²
(D) M¹L²Tâ»Â²Kâ»Â¹

Answer 1

Answer:

M¹L²T⁻²

Explanation:

[ P + a/V²] (V - b) = RT

V - b => dimensional formula of V & b will be same

V is Volume

Dimensional formula of Volume= L³

Dimensional formula of b = L³  = M⁰L³T⁰

P + a/V²

=> Dimensional formula of P  & a/V² would be same

=> Dimensional Formula of a =  Dimensional Formula of PV²

Pressure = Force / Area

Force = Mass * acceleration = M¹L¹T⁻²

Area = L²

Dimensional Formula of a = ( (M¹L¹T⁻²)/L² ) * (L³)²

= M¹L⁵T⁻²

dimensional formula of a/b = (M¹L⁵T⁻²)/(M⁰L³T⁰)

= M¹L²T⁻²

Answer 2

(P + a/V²) (V - b) = RT

WHERE  P is pressure , V is volume and T is temperature

P= F/A

=[M¹LT⁻²]/L²

=M¹L⁻¹T⁻²

V= L3

[P]=[a/V²]  

a=PV²=[M¹L⁻¹T⁻² L⁶]

=ML⁵T⁻²

a= M¹L⁵T⁻²

b= v= L³

a/b= M¹L⁵T⁻²/L³

=M¹L²T⁻²