The moment of inertia tensor of a rigid body is given by \[I = \left[ {\begin{array}{*{20}{c}} 8&0&{ - 4} \\ 0&4&0 \\ { - 4}&0&8 \end{array}} \right]\]
Moment of inertia a out an axis $${\bf{\hat n}} = \left( {\frac{1}{2},\,\frac{{\sqrt 3 }}{2},\,0} \right)$$   is

A mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius r₀ and angular speed ω₀ by an applied force $$\overrightarrow {\bf{F}} $$ communicated through an inextensible thread that passesthrough a hole on the surface as shown in figure given below. Then, this force is suddenly doubled.

The magnitude of the radial velocity of the mass

The speed of a particle whose kinetic energy is equal to its rest mass energy, is given by (c is the speed of light in vacuum)

The Hamiltonian corresponding to the Lagrangian $$L = a{{\dot x}^2} + b{{\dot y}^2} - kxy$$     is

A particle is moving in an inverse square field. If the total energy of the particle is positive, then trajectory of particle is