(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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
$\frac{M\omega L^2}{2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Rotation Motion Basic, Motion of Connected Mass

$A$ thin but rigid semicircular wire frame of radius $r$ is hinged at $O$ and can rotate in its own vertical plane. $A$ smooth peg $P$ starts from $O$ and moves horizontally with constant speed $v_0$,lifting the frame upward as shown in the figure. Find the angular velocity $\omega$ of the frame when its diameter makes an angle of $60^{\circ}$ with the vertical.

Difficult

View Solution

For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?

Easy

View Solution

Explain angular velocity and angular acceleration about a fixed axis,derive the equations of rotational motion,and write the analogy between the equations of linear motion and rotational motion.

Medium

View Solution

$A$ sphere is rotating about a diameter.

Easy

View Solution

$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

MediumMHT CET 2019

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ 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

For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?

Explain angular velocity and angular acceleration about a fixed axis,derive the equations of rotational motion,and write the analogy between the equations of linear motion and rotational motion.

$A$ sphere is rotating about a diameter.

$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

Vedclass Test Series

Exam Paper Generator

Online Exam Module