System of Parti...

A circular ring is rotating about an axis passing through its diameter. If its radius of gyration is $$10  cm$$, diameter of the ring is:

A circular disc of radius $$10 \ cm$$ is free to rotate about an axis passing through its centre without friction and its moment of inertia is $$\dfrac{1}{2}\pi  \ kg\ m^{2}$$. A tangential force of $$20  N$$ is acting on the disc along its rim.  Starting from rest, the number of rotations made by the disc in $$10 \ s$$ is:

The moment of inertia of thin rod is $$2\times 10^{-3}kgm^{2}$$ when it is made to rotate about an axis perpendicular to the length of rod and passing through one end. If half length of the rod is cut and removed then the moment of inertia of remaining rod is:

A circular disc is rotating about its own natural axis. A constant opposing torque $$2.75  N m$$ is applied on the disc due to which it comes to rest in $$28$$ rotations. If moment of inertia of disc is $$0.5  kgm^{2}$$, the initial angular velocity of disc is:

A wheel of radius $$10  cm$$ can rotate freely about an axis passing through its centre. A force $$20  N$$ acts tangentially at the rim of wheel. If moment of inertia of wheel is  $$0.5  kgm^{2}$$, its angular acceleration is:

A ceiling fan is rotating at the rate of $$3.5  rps$$ and its moment of inertia is $$1.25  kgm^{2}$$. If the current is switched off, the fan comes to rest in $$5.5  s$$. The torque acting on the fan due to friction is:

The radius of gyration of rod of length $$L$$ and mass $$M$$ about an axis perpendicular to its length and passing through a point at a distance $$\dfrac{L}{3}$$ from one of its ends is:

Identify the increasing order of the radius of gyration of following bodies of same radius:
I) About natural axis of circular ring.
II) About diameter of circular ring.
III) About diameter of circular plate.
IV) About diameter of solid sphere.

A constant torque of $$1000  N m$$ turns a wheel of moment of inertia $$200  kgm^{2}$$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $$3  s$$ is :

Identify the decreasing order of moments of inertia of the following bodies of same mass and radius.
I) about diameter of circular ring
II) about diameter of circular plate
III) about tangent of circular ring perpendicular to its plane
IV) about tangent of circular plate in its plane