Home
Class 12
PHYSICS
The general motion of a rigid body can b...

The general motion of a rigid body can be considered to be a combination of (i) a motion …. of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed `omega` , the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed `omega` in this case.

Now consider two similar systems as shown in the figure: case (a) the disc with its face vertical and parallel to x-z plane, case (b) the disc with its face making an angle of 45° with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the system are rotated with constant angular speed `omega` about the z-axis
Which of the following statement regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct ?

A

`sqrt((2g)/R)`

B

` sqrt((3g)/R)`

C

` sqrt( gR)`

D

` sqrt(g/R)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LAWS OF MOTION

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT ( SECTION -E) Assertion - Reason Type Questions|8 Videos

  • LAWS OF MOTION

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT ( SECTION -F ) Matrix - Match Type Questions|4 Videos

  • LAWS OF MOTION

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT ( SECTION -D) Linked Comprehension Type Question (Comprehension -III) (Choose the correct answer :)|3 Videos

  • KINETIC THEORY

    AAKASH INSTITUTE ENGLISH|Exercise EXERCISE (ASSIGNMENT) SECTION - D Assertion - Reason Type Questions|10 Videos

  • MAGNETISM AND MATTER

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION D)|26 Videos

Similar Questions

Explore conceptually related problems

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous exis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless, stick as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed omega the motion at any instant can be taken as a combination of (i) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed omega in this case Now consider two similar system as shown in the figure: Case (a) the disc with its face vertical and parallel to x-z plane, Case (b) the disc with its face making an angle of 45^@ with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed omega about the z-axis. Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous exis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless, stick as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed omega the motion at any instant can be taken as a combination of (i) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed omega in this case Now consider two similar system as shown in the figure: Case (a) the disc with its face vertical and parallel to x-z plane, Case (b) the disc with its face making an angle of 45^@ with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed omega about the z-axis. . Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is

A horizontal disc is rotating about a vertical axis passing through its centre. If an insect moves from centre to rim then the angular momentum of the system

Radius of gyration of a uniform circular disc about an axis passing through its centre of gravity and perpendicular to its plane is

If a circular concentric hole is made on a disc then about an axis passing through the centre of the disc and perpendicular to its plane

Derive an expression per the M.I. of a rectangular rod about an axis passing through its centre of mass and perpendicular to its length.

Radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Find its radius of gyration about a parallel axis through its centre of mass.

The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

The mass of a body cannot be considered to be concentrated at the centre of mass of the body for the purpose of computing its moment of inertia. For then the moment of inertia of every body about an axis passing through its centre of mass would be zero.