1.

In the relation P=(alpha)/(beta)e^(-alpha z//ktheta) where {:(P="pressure"),(z= "distance"), (k = "Boltzman's constant"), (theta = "Temperature"):} The dimensional formula of beta will be :

Answer»

`M^(0)L^(2)T^(0)`
`ML^(2)T`
`ML^(0)T^(-1)`
`M^(0)L^(2)T^(-1)`

SOLUTION :As exponential expression is dimensionless
`(alphaz)/(ktheta)=M^(0)L^(0)T^(0)`
`alpha=(ktheta)/(z)=(ML^(2)T^(-2)theta^(-1)xxtheta^(1))/(L^(1))`
`:.alpha=ML^(1)T^(-2).`
Now `(alpha)/(BETA)` will have dimension of `P`.
`:.beta=(alpha)/(P)=(ML^(1)T^(-2))/(ML^(-1)T^(-2))=L^(2).`
HENCE correct CHOICE is `(a)`.


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