TS EAMCET · Physics · Mechanical Properties of Fluids
An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is \(125 \%\) more than its surface area at the bottom of the tank. If the atmospheric pressure is equal to the pressure of 10 m water column, then the depth of water in the tank is
- A 16.25 m
- B 27 m
- C 19 m
- D 23.75 m
Answer & Solution
Correct Answer
(D) 23.75 m
Step-by-step Solution
Detailed explanation
\(A_t = A_b + 1.25 A_b = 2.25 A_b\) \(4\pi r_t^2 = 2.25 (4\pi r_b^2) \implies r_t = 1.5 r_b\) \(V_t = (r_t/r_b)^3 V_b = (1.5)^3 V_b = 3.375 V_b\) \(P_b V_b = P_t V_t \implies (P_{atm} + \rho g h) V_b = P_{atm} (3.375 V_b)\) \(P_{atm} + \rho g h = 3.375 P_{atm}\)…
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