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A gas bubble from an explosion under wat...

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 pressure, `d` is density of water and `E` is the total energy of the explosion. Find the value of a,b and c`.

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To solve the problem, we need to determine the values of \(a\), \(b\), and \(c\) in the proportional relationship \( T \propto P^a d^b E^c \). We will use dimensional analysis to find these values. ### Step-by-Step Solution: 1. **Identify the dimensions of each quantity:** - **Time period \(T\):** \[ ...
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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 AND is the total energy of the explosion. Find the values of a, b and, c .

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Knowledge Check

  • A gas bubble oscillates with a time period T proportional to p^(a) d^(b) E^(c) where P is pressure , d is the density and E is the energy. The values of a,b and C are :

    A
    `a=3/2 , b=-1/3, c =1/2`
    B
    `a=-5/6, b=1/3,c=1/2`
    C
    `a=-5/6, b=1/2, c=1/3`
    D
    `a=3/2, b=-1/3, c=1/2`

  • A dubble under water oscillates with period T, which is proportional to p^(-5//6),d^(1//2)E^(Y), where p is pressure, d is density and E is energy. The value of gamma is -

    A
    `(1)/(7)`
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    `(1)/(6)`
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    `(1)/(3)`

  • The period T of a soap bubble under SHM is given by T = P^(a) D^(b) S^(c ) , where P is pressure, D , is density and S is surface tension. Then the values of a,b and c are

    A
    `- (3)/(2), (1)/(2), 1`
    B
    `-1, -2, 3`
    C
    `(1)/(3), - (3)/(2), - 1//2`
    D
    `1, 2, (3)/(2)`

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