Advertisements
Advertisements
प्रश्न
The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4MR2 where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane.
Advertisements
उत्तर
- M.I. of a uniform circular disc about a tangent in its own plane, I1 = `5/4`MR2
- Applying parallel axis theorem
I1 = I2 + Mh2
∴ I2 = I1 – MR2 = `5/4`MR2 - MR2 = `("MR"^2)/4` - Applying perpendicular axis theorem,
I3 = I2 + I2 = 2I2
∴ I3 = `2 xx ("MR"^2)/4 = ("MR"^2)/2`
APPEARS IN
संबंधित प्रश्न
A diver in a swimming pool bends his head before diving. It ______.
The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of the loop is ______
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?
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 ______.
A uniform disc of radius ' a' and mass 'm' is rotating freely with angular speed 'ω' in a horizontal plane, about a smooth fixed vertical axis through its centre. A pa1ticle of mass 'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular speed is ______
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)
The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of L/3 from one of its ends and perpendicular to the rod is ______
Two rods, each of mass m and length l, are joined as shown in the figure. Moment of inertia of system about an axis passing through one end of the rod, i.e. O, and perpendicular to the plane 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.
From a disc of mass 'M' and radius 'R', a circular hole of diameter 'R' is cut whose rim passes through the center. The moment of inertia of the remaining part of the ruse about perpendicular axis passing through the center 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)
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 ____________.
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 ______.
A disc rolls down a smooth inclined plane without slipping. An inclined plane makes an angle of 60° with the vertical. The linear acceleration of the disc along the inclined plane is ______.
(g = acceleration due to gravity, sin 30° =cos 60° `=1/2,` sin 60° = cos 30° `=sqrt3/2`)
The moment of inertia of a circular disc of mass M and radius R about an axis passing through the centre of mass is I0. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis 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 ______.
A disc of radius R and thickness `"R"/6` has moment of inertia/about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is ______.
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is ______.
Two discs A and B of same material and thickness have radii R and 3R respectively. Their moments of inertia about their axis will be in the ratio ______.
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 ______.
Four point masses, each of mass ‘m’ are arranged in X-Y plane as shown in the figure. The moment of inertia of this system about X-axis is:
