The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is

A. $${\text{T}} = \frac{{2\omega }}{{{\pi ^2}}}$$ B. $${\text{T}} = \frac{{2\pi }}{\omega }$$ C. $${\text{T}} = \frac{2}{\omega }$$ D. $${\text{T}} = \frac{\pi }{{2\omega }}$$

A. 0.1 rad/sec B. 1 rad/sec C. 10 rad/sec D. 100 rad/sec

A. Always directed away from the centre, the point of reference B. Proportional to the square of the distance from the point of reference C. Proportional to the distance from the point of reference and directed towards it D. Inversely proportion to the distance from the point of reference

A. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{P}}\sin \theta $$ B. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta $$ C. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\tan \theta $$ D. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta } $$ E. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\sin \theta } $$