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A gas bubble, from an exlosion under wat...

A gas bubble, from an exlosion 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 `'E'` is the total energy of the explosion. Find the values of `a, b and, c`.

Text Solution

Verified by Experts

Given that,
`T prop p^(a)d^(b)E^(c)`
Equating both sides dimensionally,
`[T]=[ML^(-1)T^(-2)]^(d)[ML^(-3)]^(b)[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 exponents of similar quantities,
`a+b+c=0," "-a-3b+2c=0` and `-2a-2c=1`
Solving these for a, b and c, we get
`a=-5/6," "b=1/2" "` and `c=1/3`
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