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A cylindrical vessel containing a liquid is rotated about its vertical axis so that the liquid rises at its sides, as shown in the figure: the free surface dips at the axis and climbs at the wall, and h is the height of the wall level above the level at the centre. The radius of the vessel is 5 cm and the angular speed of rotation is ω rad s⁻¹. The difference in height, h (in cm), of the liquid at the centre of the vessel and at the side will be

Asked in JEE Main 2nd Sept 1st Shift 2020 · Rotating and accelerating fluids

• (1) (2ω²)/(25g)
• (2) (5ω²)/(2g)
• (3) (25ω²)/(2g)
• (4) (2ω²)/(5g)

Step-by-step solution

Why the other options are wrong

• (1) comes from is (R²)/(2g) written upside down as 2/(R²g); the tell is that it makes h smaller for a wider vessel, whereas a wider vessel throws the liquid further out and raises the rim more.
• (2) comes from uses R instead of R², putting 5 where 25 belongs; the centripetal acceleration ω²r has to be integrated across the radius, and that integration is what squares R.
• (4) comes from combines both slips of options 1 and 2 — the radius not squared and the fraction inverted — which is why it is the smallest of the four expressions.

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