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. `a=3/2 , b=-1/3, c =1/2`
B. `a=-5/6, b=1/3,c=1/2`
C. `a=-5/6, b=1/2, c=1/3`
D. `a=3/2, b=-1/3, c=1/2`

Answer

3

Explanation

[T]=[P]a[d]b[E]c
`M^(0) L^(0) T^(1) =(ML^(-1)T^(-2))^(a) (ML^(-3))^(b) (ML^(2) T^(-2))^(c)`
`rArr a+b+c=0....(i)`
`-a-3b+2c=0,.....(ii)`
`-2a-3b-2c=1....(iii)`
`rArr a=(-5)/6, b=1/2 , c=1/3`