Home
Class 12
PHYSICS
At any instant, a rolling body may be co...

At any instant, a rolling body may be considered to be in pure rotation about an axis through the point of contact. This axis is translating forward with speed

A

equal to centre of mass

B

zero

C

twice of centre of mass

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

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?

Torques of equal magnitude are applied to hollow cylinder and a solid sphere, both having the same mass and same radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. which of the two will acquire a greater angular speed after a given time ?

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

The axis of rotation of a purely rotating body

Assertion : Speed of any point on rigid body executing rolling motion can be calculated by expression v =r omega , where r is distance of point from instantaneous centre of rotation Reason : Rolling motion of rigid body can be considered as a pure rotation about instantaneous centre of rotation.

Consider three bodies : a ring, a disc and a sphere. All the bodies have same mass and radius. All rotate about their axis through their respective centre of mass and perpendicular to the plane. What is the ratio of moment of inertia ?

Two identical rings each of mass m with their planes mutually perpendicular, radius R are welded at their point of contact O . If the system is free to rotate about an axis passing through the point P perpendicular to the plane of the paper, then the moment of in inertia of the system about this axis is equal to

(1) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts, (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius, (3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.., (4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. which one of the following pairs of statements is correct ?

Let the transverse axis ofa varying hyperbola be fixed with length of transverse axis being 2a. Then the locus of the point of contact of any tangent drawn to it from a fixed point on conjugate axis is