Consider a planet whose density is same as that of the earth but whose radius is three times the radius '$$R$$' of the earth. The acceleration due to gravity '$$\mathrm{g}_{\mathrm{n}}$$' on the surface of planet is $$\mathrm{g}_{\mathrm{n}}=\mathrm{x}$$. $$\mathrm{g}$$ where $$\mathrm{g}$$ is acceleration due to gravity on surface of earth. The value of '$$\mathrm{x}$$' is

When a certain metal surface is illuminated with light of frequency $$v$$, the stopping potential for photoelectric current is $$\mathrm{V}_0$$. When the same surface is illuminated by light of frequency $$\frac{v}{2}$$, the stopping potential is $$\frac{\mathrm{V}_0}{4}$$, the threshold frequency of photoelectric emission is

If the length of an open organ pipe is $$33.3 \mathrm{~cm}$$, then the frequency of fifth overtone is [Neglect end correction, velocity of sound $$=333 \mathrm{~m} / \mathrm{s}$$ ]

A transparent glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $$10 \mathrm{~cm}$$ from the surface. When seen normally from opposite surface, its apparent distance is $$6 \mathrm{~cm}$$. The distance of the air bubble from first surface is