Question

A thin rod AB of mass $M$ and length $L$ is rotating with angular speed ${\omega }_0$ about vertical axis passing through its end B on a horizontal smooth table as shown. If at some instant the hinge at end B of rod is opened then which of the following statements is/are correct about motion of rod.

• A. The angular speed of rod after opening the hinge will remain ${\omega }_0$
• B. The angular speed of rod after opening the hinge will be less than ${\omega }_0$
• C. In the process of opening the hinge the kinetic energy of rod will remain conserved.
• D. Angular momentum of rod will remain conserved about centre of mass of rod in the process of opening the hinge.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The angular speed of rod after opening the hinge will remain ${\omega }_0$
C In the process of opening the hinge the kinetic energy of rod will remain conserved.
D Angular momentum of rod will remain conserved about centre of mass of rod in the process of opening the hinge.

As no external torque is present, there is no angular acceleration and thus angular velocity remains constant. Also as the angular velocity is constant the kinetic energy too remains conserved. Also by definition, for no external torque the angular momentum about the center of mass remains conserved.