Advertisements
Advertisements
Question
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is ______.
Options
`"MR"^2/4`
`"MR"^2/2`
MR2
`(3"MR"^2)/2`
Advertisements
Solution
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is `underlinebb("MR"^2/2)`.
APPEARS IN
RELATED QUESTIONS
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, then what is the ratio of their angular velocity.
The moment of inertia of a body about a given axis is 1.2 kgm2. initially, the body is at rest. For what duration on the angular acceleration of 25 radian/sec2 must be applied about that axis in order to produce rotational kinetic energy of 1500 joule?
Two wheels of the moment of inertia 4 kgm2 rotate side by side at the rate of 120 rev/min and 240 rev/min respectively in the opposite directions. If now both the wheels are coupled by means of a weightless shaft so that both the wheels rotate with a common angular speed. Calculate the new speed of rotation.
A thin uniform rod has mass M and length L The moment of inertia about an axis perpendicular to it and passing through the point at a distance `"L"/3` from one of its ends, will be ______.
Surface density of charge on a charged conducting sphere of radius R in terms of electric field intensity E at a distance r in free space is ____________.
(r > R, ε0 = permittivity of free space)
Three points masses, each of mass m are placed at the corners of an equilateral triangle of side l. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be ______.
If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is ______.
Four solid spheres each of mass M and radius R are placed with their centres on the four comers of a rectangle. If b is a breadth of rectangle and its length is twice of its breadth, then find moment of inertia of the system about an axis along one of the breadth of the rectangle.
Three identical rods each of mass 'M' and length 'L' are joined to form a symbol 'H'. The moment of inertia of the system about one of the sides of 'H' is ______.
A flywheel of mass 20 kg and radius 5 cm is revolving at a speed of 300 rpm. Its kinetic energy is ______.
If I1 is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and I2 is the moment of inertia of the ring formed by bending the rod about an axis perpendicular to the plane, the ratio of I1 and I2 is ____________.
Moment of inertia of earth about its axis of rotation is ____________.
A cord is wound round the circumference of a wheel of radius 'r'. The axis of the wheel is horizontal and moment of inertia about it is T. A block of mass 'm' is attached to free end of the cord, initially at rest. When the wheel rotates and the block moves vertically downwards through distance 'h', the angular velocity of the wheel will be ______.
(Neglect the mass of cord, g =acceleration due to gravity)
The moment of inertia of a body initially at rest about a given axis is 1.2 kg m2. On applying an acceleration of 25 rad/s2, the time it will take to acquire a rotational kinetic energy of 1500 J is ____________.
Three rings, each of mass P and radius Q, are arranged as shown in the figure. The moment of inertia of the arrangement about YY' will be ______.

The moment of inertia of a sphere is 20 kg-m2 about the diameter. The moment of inertia about any tangent is ____________.
A thin uniform rod of length 'L' and mass 'M' is bent at the middle point 'O' at an angle of 45° as shown in the figure. The moment of inertia of the system about an axis passing through 'O' and perpendicular to the plane of the bent rod, is ______.

Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis ______.

A uniform disc of mass 4 kg has radius of 0.4 m. Its moment of inertia about an axis passing through a point on its circumference and perpendicular to its plane is ______.
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is ______.
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce, a rotational kinetic energy of 1500 J, an acceleration of 25 rad/s2 must be applied about that axis for a duration of ______.
Two spheres each of mass M and radius R are connected with a massless rod of length 4 R. The moment of inertia of the system about an axis passing through the centre of one ofthe spheres and perpendicular to the rod will be ______.

If two circular rings A and B are of same mass but of radii r and 2r respectively, then the moment of inertia about an axis passing through C.G. and perpendicular to its plane, of A is ______.
