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.
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
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 ______
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 ______.
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 ______
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 ______.
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.
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 particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s2 is ______.
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)
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 ____________.
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 ______.
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 ______.
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 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 ______.
