KE of a rotating body is given by `1/2 I omega^2`,where l is moment of inertia and `omega` is nagular velocity of the body.Find the dimensions of I.

A body of momentum of inertia I has an angular momentum L.The rotational KE of the body is :

Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR^2//4 , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

If a composite physical quantity in terms of moment of inertia I, force F, velocity v, work W and length L is defined as Q = (iFv^2)/(WL^3) , find dimensions of Q and identify it.

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

A rigid body is spinning about a fixed point (3,-2,-1) with an angular velocity of 4 rad/s, the axis of rotation being in the direction of (1,2,-2). Find the velocity of the particle at point (4,1,1).

Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2//5 , where M is the mass of the sphere and R is the radius of the sphere.

A body describessimple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 5 cm.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 3 cm.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 0 cm.

A 2 kg body and a 3 kg body are moving along X-axis. At a particular instnat, the 2 kg body is 1 m from the origin and has a velocity of 3 ms^-1 and the 3 kg body is 2 m away from the origin has a velocity of -1 ms^-1 . Find the position and velocity of the centre of mass.