A gas bubble , from an explosion under water , oscillates with a period T proportional in `P^(a)D^(b)E^(c)` , where p is the static pressure , d is the density of water and E is the total energy of the explosion . Find the value of` a , b` and` c` .

Answer

A, B, C

Explanation

Given that `T prop P^(a)d^(0)E^( c )`
rArr `[M^(0)L^(0)T^(1)] = [ ML^(-1)T^(-2)]^(a) [ML^(-3)]^(b)[ML^(2)T^(-2)]^( c )]`
:. `[M^(0)L^(0)T^(1)] = [ M^(a + b + c)L^(-a - 3b + 2c)T^(-2a - 2c)]`
`a + b + c = 0, - a - 3b + 2c = 0`,
`- 2a - 2c = 1` On solving, we get
`a = - 5//6, b = 1//2, c = 1//3`