Show that (P^(-5//6)rho^(1//2)E^(1//3)) is of the dimension of time. Here P is the pressure, rho is the density and E is the energy of a bubble).

Show that (P^(-5//6)rho^(1//2)E^(1//3)) is of the dimension of time. H

1.	Show that (P^(-5//6)rho^(1//2)E^(1//3)) is of the dimension of time. Here P is the pressure, rho is the density and E is the energy of a bubble).
Answer» Solution :DIMENSION of Pressure = `[ML^(-1)T^(-2)]` Dimension of density = `[ML^(-3)]` Dimension of Energy = `[ML^(2)T^(-2)]` By SUBSTITUTING in the given equation, `=[ML^(-1)T^(-2)]^(-5//6) [ML^(-3)]^(1//2) [ML^(2)T^(-2)]^(1//3)` `= M^(-5//6+1//2+1//3) L^(5//6-3//2+2//3)T^(5//3-2//3)` `= M^(0)L^(0)T^(1) = [T]`