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A small spherical monoatomic ideal gas b...

A small spherical monoatomic ideal gas bubble `(gamma=5//3)` is trapped inside a liquid of density `rho` (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is `T_0`, the height of the liquid is H and the atmospheric pressure `P_0` (Neglect surface tension).

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

A

`rho_(1)nRgT_(0)((P_(0)+rho_(1)gH)^(2//5))/((P_(0)+rho_(1)gy)^(7//5))`

B

`(rho_(1)RgT_(0))/((P_(0)+rho_(1)gH)^(2//5){P_(0)+rhog(H-y)}^(3//5))`

C

`rho_(1)nRgT_(0)((P_(0)+rho_(1)gH)^(3//5))/((P_(0)+rho_(1)gy)^(8//5))`

D

`(rho_(1)RgT_(0))/((P_(0)+rho_(1)gH)^(3//5){P_(0)+rhog(H-y)}^(2//5))`

Text Solution

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The correct Answer is:
B
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