The diameter of a gas bubble formed at the bottom of a pond is d = 4.0 μm. When the bubble rises to the surface its diameter increases to n = 1.1 times. Depth of pond is x metre. The nearest integer to x is _____. (Atmospheric pressure is 10 m of water column; gas expansion is isothermal.)
Physics · Mixed Chapter
JEE Mains

Question

The diameter of a gas bubble formed at the bottom of a pond is d = 4.0 μm. When the bubble rises to the surface its diameter increases to n = 1.1 times. Depth of pond is x metre. The nearest integer to x is _____. (Atmospheric pressure is 10 m of water column; gas expansion is isothermal.)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Gas volume ∝ diameter³. On rising, V_surface/V_bottom=(1.1)³=1.331. Step 2: For isothermal expansion, P_bottom V_bottom=P_surface V_surface. In equivalent metres of water, P_surface=10 and P_bottom=10+x. Step 3: (10+x)/10=1.331, so x=3.31 m. Step 4: Nearest integer is 3.