Question

time period of oscillation of gas bubble depends upon pressure , density and energy. find dimensionally equation for time period. ​

Answer 1

Given time period T
T∝P
a
d
b
E
c


T=kP
a
d
b
E
c
.....eq(1)
where K is a constant of proportionality and dimensionless quantity.

Inserting the dimensions of Time, pressure, density and Energy in equation (1) we get
[T]=[ML −1 T −2] a
[ML −3] b
[ML 2T −2] c


Equating powers of M ,L,T on both sides we get
0=a+b+c ...(2)
0=−a−3b+2c ..(3)
1=−2a−2c ..(4)

A=-5/6, B=1/2, C=1/3

Answer 2

Answer:

Explanation:

Given time period T

T∝P  ^a D^b E^c

T = k P^a D^b E^c------ (1)

where K is a constant of proportionality and dimensionless quantity.

Inserting the dimensions of Time, pressure, density and Energy in equation (1) we get,

( rest of the explanation sice I am tired of typing I am putting a pic below )

hope it help u