The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$ . Its angular momentum, with respect to the origin, at time t = 2 is

A thin disc of mass M and radius R has mass per unit area $$\sigma $$(r) = kr² where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :

Two coaxial discs, having moments of inertia I₁ and I₁/2, are rotating with respective angular velocities $$\omega $$₁ and $$\omega $$₁/2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E_f and E_i are the final and initial total energies, then (E_f - E_i) is:

A particle of mass m is moving along a trajectory given by
x = x₀ + a cos$$\omega $$₁t
y = y₀ + b sin$$\omega $$₂t
The torque, acting on the particle about the origin, at t = 0 is :