A gas bubble , from an explosing under water , oscillates with a period T proportional in P^(0)D^(0)E^(0) , where p is the static prossure , d is the density of water and E is the total energy of the explosion . Find the value of a , b and c .
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The value of a is -7/6, b is -1/2 and c is 2/3
Static pressure of bubble = p = ML`−1T`−2
Density of water = d =ML`−3
Energy of explosion = E = ML²T`−2]
Therefore,
[T] = [p`ad`bE`c] =[ML`−1T`−2]`0[ML`−3]`4[ML²T`−2]`1
Equating the power of both sides , we have
since, a+b+c=0
−a−3b+2c=0
a = 3b+2c
Therefore, (3b+2c)+b+c=0
4b + 3c = 0
b = -3c/4
-2a - 2c = 1
a = -1+2c/2
Thus, 1+22c/2 - 3c/4+c = 0
On solving - a = -7/6, b = -1/2 and c = 2/3
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