A force of $$-\mathrm{P} \hat{\mathrm{k}}$$ acts on the origin of the coordinate system. The torque about the point $$(2,-3)$$ is $$\mathrm{P}(a \hat{i}+b \hat{j})$$, The ratio of $$\frac{a}{b}$$ is $$\frac{x}{2}$$. The value of $$x$$ is -

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $$3 \mathrm{~m} / \mathrm{s}$$ (as shown in figure). Maximum height with respect to the initial position covered by it will be __________ cm.

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $$\frac{1}{x} \mathrm{MR}^{2}$$, where $$\mathrm{R}$$ is the radius and $$M$$ is the mass of the semicircular ring. The value of $$x$$ will be __________.

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $$\sqrt{\frac{2}{x}}$$. The value of $$x$$ is ___________.