(A) Consider a small element of the liquid of length $dx$ at a distance $x$ from the axis of rotation.The mass of this small element is $dm = (M/L) dx

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(A) Consider a small element of the liquid of length $dx$ at a distance $x$ from the axis of rotation.The mass of this small element is $dm = (M/L) dx$.The centrifugal force $dF$ acting on this element is $dF = (dm) x \omega^2 = (M/L) x \omega^2 dx$.To find the total force exerted by the liquid on the other end,we integrate this expression from $x = 0$ to $x = L$:$F = \int_0^L \frac{M}{L} \omega^2 x dx = \frac{M \omega^2}{L} \left[ \frac{x^2}{2} \right]_0^L = \frac{M \omega^2}{L} \cdot \frac{L^2}{2} = \frac{ML\omega^2}{2}$.

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

Difficult

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

A
$\frac{ML\omega^2}{2}$
B
$ML\omega^2$
C
$\frac{M\omega^2L^2}{2}$
D
$\frac{M\omega L^2}{2}$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

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

Similar Questions

$A$ uniform rod is rotating in a gravity-free region with a certain constant angular velocity $\omega$. The variation of tensile stress $\sigma$ with distance $x$ from the axis of rotation is best represented by which of the following graphs?

What is a rigid body? Explain the concept of a rigid body.

For every particle of a rigid body in rotational motion,which of the following is true?

$A$ mass $m$ is suspended from a string wrapped around a frictionless pulley. The pulley has a mass $M$ and radius $R$. If the pulley is a uniform circular disk and the string does not slip on the pulley,what is the acceleration of the mass?

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