In figure $$E$$ and $$v_{\mathrm{cm}}$$ represent the total energy and speed of centre of mass of an object of mass $$1 \mathrm{~kg}$$ in pure rolling. The object is

A wheel starting from rest gains an angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ after uniformly accelerated for $$5 \mathrm{~s}$$. The total angle through which it has turned is

A thin uniform rectangular plate of mass $$2 \mathrm{~kg}$$ is placed in $$x y$$-plane as shown in figure. The moment of inertial about $$x$$-axis is $$I_x=0.2 \mathrm{~kgm}^2$$ and the moment of inertia about $$Y$$-axis is $$I_y=0.3 \mathrm{~kgm}^2$$. The radius of gyration of the plate about the axis passing through $$O$$ and perpendicular to the plane of the plate is

A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from $$A$$ to $$B$$, the angular momentum of the particle about $$O$$