A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the side. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/sec. Find the difference in the height of the liquid at the centre of the vessel and its sides (in cm). (g = 9.86 m/s²)
Physics · Mixed Chapter
JEE Mains

Question

A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the side. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/sec. Find the difference in the height of the liquid at the centre of the vessel and its sides (in cm). (g = 9.86 m/s²)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Angular speed is ω=2×2π=4π rad/s. The steady free surface is paraboloidal: z(r)−z(0)=ω²r²/(2g). Step 2: At vessel radius R=0.05 m, Δh=(4π)²(0.05)²/(2×9.86)≈0.0200 m. Step 3: Convert to centimetres: Δh≈2.0 cm. Correct numerical answer: 2.