Question

a gas bubble from an explotion under water oscillates with a period t propotional to density of water static pressure and total energy of exploitation find the values of a b c

Answer 1

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given,

T ∝ Pa db Ec

 = K Pa db Ec  ( K being some constant)

putting the dimensions of pressure,density,energy and time

[ T ] = K[M L-1 T-2]a [M L-3 ]b [M L2 T-2]c

 = K [ M ]a+b+c [ L ]-a-3b+2c[ T ]-2a-2c

compairing powers on LHS and RHS

a+b+c = 0  ...........................(1)

-a-3b+2c = 0  ............................(2)

-2a-2c = 1  ............................(3)

from (3)

 a+c = -1/2

or,     c = -1/2 - a

putting in (1) gives b= 1/2

from (2)

 

-a -3(1/2) + 2(-1/2 - a) = 0

or,          a= -5/6

 

from (3)

-2(-5/6) - 2c = 1

or, 5/3 -2c = 1

or, 2c = 5/3 - 1

or, c = 1/3


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