A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be

Question

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be (A) 1.2 (B) 0.1 (C) 2.0 (D) 0.4

Tardigrade Admin · Accepted Answer

y = (ω2 x2/2g) = ((2 × 2π)2 ×(0.05)2/20)] ≃ 2 cm

1.2

0.1

2.0

0.4

y=2gω2x2​=20(2×2π)2×(0.05)2​]≃2cm

$y = \frac{ω ^{2} x ^{2}}{2 g} = \frac{( 2 \times 2 π ) ^{2} \times ( 0.05 ) ^{2}}{20}] ≃ 2 c m$