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A gas bubble from an explosion under wat...

A gas bubble from an explosion under water oscillates with a period proportional to `P^(a)d^(b)E^(c),` where `P` is the static pressure, `d` is the density of water and `E` is the energy of explosion. Then a,b,c are respectively :

A

`1,1,1`

B

`(1)/(3),(1)/(2),(-5)/(6)`

C

`(-5)/(6),(1)/(2),(1)/(3)`

D

`(1)/(2),(-5)/(6),(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `T=P^(a)d^(b)E^(c)`
Writing dimensions on both sides,
`[M^(0)L^(0)T^(0)]=[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)`
Thus `a+b+c=0,-a-3b+2c=0,-2a-2c=0.`
On solving eqns, we get `a=(-5)/(6),b=(1)/(2)` and `c=(1)/(3)`
Hence the correct `(c )`.
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