JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Laws of Motion

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A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity

x F rad s^{- 1}

. If F be the force exerted by the liquid at the other end then the value of x will be ____.

Answer: 4

Solution

The force exerted by the liquid at the far end is due to centrifugal effect:

F = \int_{0}^{L} (d m) ω^{2} x = \int_{0}^{L} \frac{m}{L} d x \cdot ω^{2} x = \frac{m ω ^{2} L}{2}

Solving for

ω

ω = \frac{2 F}{m L}

Given

ω = x F

, we have:

x F = \frac{2 F}{m L}

x = \frac{2}{m L} = \frac{2}{0.25 \times 0.5} = 16 = 4

The answer is 4.

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Integer answer

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