A gas bubble from an explosion under water oscillates with a period T proportional to 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 explosion. Find the value of a,b and c.

A gas bubble from an explosion under water oscillates with a period T

1.	A gas bubble from an explosion under water oscillates with a period T proportional to 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 explosion. Find the value of a,b and c.
Answer» Solution :`Tprop p^(a)d^(b)E^(c)` `T=kp^(a)d^(b)E^(c)` TAKING dimensions on both sides `T=[ML^(-1)T^(-2)]^(a)[ML^(-3)]^(b)[ML^(2)T^(-2)]^(c)` `M^(0)L^(0)T=M^(a+b+c)L^(-a-3b+2c)T^(-2a-2c)` Equating the dimensions of M,L and T `a+b+c=0, ""-a-3b+2c=0,""-2a-2c=1` Solving `a=-5/6, b=1/2` and `c=1/2` So we GET `T=kp^(-5//6)d^(1//2)E^(1//2)` or `Tprop p^(-5//6)d^(1//2)E^(1//2)`