Physics Circle home Student Login

Home›Chapters›Fluid Statics PYQs›Pressure in a Fluid›Question 25

JEE Main 2018 (15 Apr, Shift 2) · Pressure in a Fluid

Pressure in a Fluid question from JEE Main 2018 (15 Apr, Shift 2)

Q25JEE Main 2018 · 15 APR · SHIFT 2Difficult

Pressure in a Fluid

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes 5r4\frac{5r}{4} Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

Show answer and solution

Answer: (c)

  1. Volume ratio: V2V1=(54)3=12564\dfrac{V_2}{V_1} = \left(\dfrac{5}{4}\right)^3 = \dfrac{125}{64}.
  2. Boyle's law in water-column units: (10+h)×64=10×125(10 + h)\times64 = 10\times125
  3. 10+h=19.53⇒h≈9.5 m10 + h = 19.53 \Rightarrow h \approx 9.5\text{ m}
  4. So the answer is (c) 9.5 m.
Report a mistake

More questions on Pressure in a Fluid