A gas bubble, from an explosion under water, oscillates with a period proportional to `P^a d^b E^c`, where P is the static pressure , d is the density and E is the total energy of the explosion. Find the values of a,b and c.

Options

A. `-(5)/(6), (1)/(2), (1)/(3)`
B. `- (1)/(3), (1)/(3), (1)/(4)`
C. `(1)/(3), (1)/(2), -(5)/(6)`
D. `-(5)/(6), (1)/(3), (1)/(2)`

Answer

C

Explanation

`T prop P^(a)b^(b)E^(c )`
By dimensional analtsis
`[T] = [ML^(-1)T^(_2)]^(a) [ML^(-3)]^(b) [ML^(2)T^(-2)T^(-2)]^(c )`
Solving for a, b, c, we get
`a = -(5)/(6), b = (1)/(2), c = (1)/(3)`