Question

It is given that the time period (T) of oscillation, of a gas bubble, formed under water, depends upon pressure (P), density (d) and energy (E), as

T = kp^a d^b E^c

The value of a, b and c, are:

(1) (-5/6), (1/2) and (1/3)

(2) (-5/6), (1/3) and (1/2)

(3) (5/6), (1/3) and (1/2)

(4) (5/6), (1/2) and (1/3)

Answer 1

(1) (-5/6), (1/2) and (1/3)

Putting dimensions, of all the terms, in the relation.

T = kp^a d^b E^c , we get

[T] = [ML^-1T^-2]^a [ML^-3]^b [ML²T^-2]^c

∴ a + b + c = 0 

- a - 3b + 2c = 0 

-2a - 2c = 1 

These equations give, 

a = -5/6, b = 1/2, c = 1/3