SATHEE: Rotation 5 Question 9

Rotation 5 Question 9

19. A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $ω$ . The force exerted by the liquid at the other end is

(a) $\frac{M ω^{2} L}{2}$

(b) $M ω^{2} L$

(d) $\frac{M ω^{2} L^{2}}{2}$

(1992, 2M)

Objective Question II (One or more correct option)

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Answer:

Correct Answer: 19. (a)

Solution:

Mass of the element $d x$ is $m = \frac{M}{L} d x$ .

This element needs centripetal force for rotation.

$\begin{array}{ll} ∴ & d F = m x ω^{2} = \frac{M}{L} x ω^{2} d x \\ ∴ & F = \int_{0}^{L} d F = \frac{M}{L} \cdot ω^{2} \int_{0}^{L} x d x = \frac{M ω^{2} L}{2} \end{array}$

This is the force exerted by the liquid at the other end.

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Rotation 5 Question 9

19. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

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19. A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $ω$ . The force exerted by the liquid at the other end is