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JEE Advanced2008PhysicsMechanical Properties of FluidsActual

Paragraph: A small spherical monoatomic ideal gas bubble ( = 5 3 ) is trapped inside a liquid of density ₁ (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 T₀ , the height of the liquid is H and the atmospheric pressure is p₀ (Neglect surface tension). Question: The buoyancy force acting

Options

  1. A_l n R g T₀ ( ₀+ _l g H )^ 2 5 ( ₀+ _l g y )^ 7 5
  2. B_l n R g T₀ ( ₀+ _l g H )^ 2 5 [ ₀+ _l g(H-y) ]^ 3 5
  3. Cn R g T₀ ( ₀+ _l g H )^ 3 5 ( ₀+ _l g y )^ 8 5
  4. D_l n R g T₀ ( ₀+ _l g H )^ 3 5 [ ₀+ _l g(H-y) ]^ 2 5

Correct answer

B. _l n R g T₀ ( ₀+ _l g H )^ 2 5 [ ₀+ _l g(H-y) ]^ 3 5

Step-by-step solution

Buoyancy force Here, and aligned F & =( volume of bubble ) ( _l ) g & = ( n R T₂ p₂ ) p_l g T₂ & =T₀ [ p₀+p_l g(H-y) p₀+ _l g H ] p₂ & =p₀+p_l(H-y) aligned Substituting the values we get, F= _n n g T₀ (p₀+ _l g H )^ 2 / 5 [p₀+ _l g(H-y) ]^ 3 / 5 correct option is (b).

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