An undersea experiment went wrong and the entire station blew up with an energy E. This released air bubbles with static pressure p. One such air bubble oscillated with a period T (found to be proportional to pa db Ec) where d is the density of water. Find the values of a, b and c.
Time period is given by:
Dimension are:
where p is pressure = [M1L-1T-2]
d is the density = [M1L-3T0]
E is energy = [M1L2T-2]
Time period = [M0L0T1]
According to the formula:
[M0L0T1] = [M0L0T1]a [M1L-3T0]b [M1L2T-2]c
= [Ma+b+c] [Lb-3c] [T-2a-2c]
equating the power of LHS and RHS,
we get,
a =5/6
b = -1/2
c = -1/3
Dimension are:
where p is pressure = [M1L-1T-2]
d is the density = [M1L-3T0]
E is energy = [M1L2T-2]
Time period = [M0L0T1]
According to the formula:
[M0L0T1] = [M0L0T1]a [M1L-3T0]b [M1L2T-2]c
= [Ma+b+c] [Lb-3c] [T-2a-2c]
equating the power of LHS and RHS,
we get,
a =5/6
b = -1/2
c = -1/3