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 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 particle starting from rest moves along the circumference of a circle of radius r with angular acceleration a. The magnitude of the average velocity, in the time it completes the small angular displacement θ 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)
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 ______.
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 ______.
Moment of inertia of earth about its axis of rotation 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 ____________.
A rod of length 1 m and mass `1/2` kg rotates at an 2 angular speed of 6 rad s-1 about one of its ends. The kinetic energy of the rod is ______.
The moment of inertia of a sphere is 20 kg-m2 about the diameter. The moment of inertia about any tangent is ____________.
Two discs having moment of inertia I1 and I2 are made from same material have same mass. Their thickness and radii are t1, t2, and R1, R2 respectively. The relation between moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is ______.
Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis ______.
Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is 'I1'. The same rod is bent into a ring and its moment of inertia about the diameter is 'I2', then `"I"_2/"I"_1` is ______.
The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is 'I'. It is rotating with angular velocity 'ω'. Another identical ring is gently placed on it so that their centres coincide. If both the ring are rotating about the same axis, then loss in kinetic energy is ______.
Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its center.
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 ______.
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 ______.
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:
