A gas bubble, from an exlosion under water, oscillates with a period `T` proportional to p^(a)d^(b)E^( c )`. Where `'P'` is the static pressure, `'d'` is the density of water `'E'` is the total energy of the explosion. Find the values of `a, b and, c`.

Options

A. `a = 0, b = 1, c = 2`
B. `a = 1, b = 2, c = 3`
C. `a=5//6, b=-1//2, c=1//3`
D. `a=5//6, b=-1//2, c=1//3`

Answer

d

Explanation

`T prop P^(a)d^(b)E^(c)`
`[M^(0)L^(0)T]=[ML^(-1)T^(-2)]^(a)[ML^(-3)]^(b)[ML^(2)T^(-2)]^(c)`
Comparing dimensions of M, L and T solving,
`a=-5//6, b=1//2, c=1//3`.