A stone is projected vertically upwards with velocity 'V. Another stone of same mass is projected at an angle fo $$60^{\circ}$$ with the vertical with the same speed $$(\mathrm{V})$$. The ratio of their potential energies at the highest points of their journey, is

$$\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]$$

A glass slab has refractive index '$$\mu$$' with respect to air and the critical angle for a ray of light in going from glass to glass to air is '$$\theta$$' If a ray of light is incident from air on the glass with angle of incidence '$$\theta$$', then the corresponding angle of refraction is

A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube $$=1 \mathrm{~cm}, \eta=1 \times 10^{-3} \frac{\mathrm{Ns}}{\mathrm{m}^2}, R_n=2500$$ and density of water $$=10^3 \mathrm{~kg} / \mathrm{m}^3$$]

A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?