The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

A sphere of radius $R$ is cut from a larger solid sphere of radius $2 R$ as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the $Y$-axis is:

The radius of gyration of a solid sphere of mass $$5 \mathrm{~kg}$$ about $$X Y$$ is $$5 \mathrm{~m}$$ as shown in figure. The radius of the sphere is $$\frac{5 x}{\sqrt{7}} \mathrm{~m}$$, then the value of $x$ is:

A bob is whirled in a horizontal plane by means of a string with an initial speed of $$\omega \mathrm{~rpm}$$. The tension in the string is $$T$$. If speed becomes $$2 \omega$$ while keeping the same radius, the tension in the string becomes: