A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm^–1, density = 667 kg m^–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60^o with one another. Then h is close to (g = 10 ms^–2)

A wire of density 9 $$ \times $$ 10^–3 kg cm^–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 $$ \times $$ 10^–4. The lowest frequency of the transverse vibrations in the wire is : (Young’s modulus of wire Y = 9 $$ \times $$ 10¹⁰ Nm^–2), (to the nearest integer), _________

A light ray enters a solid glass sphere of refractive index $$\mu $$ = $$\sqrt 3 $$ at an angle of incidence 60^o. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ________.

A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If $$\sin {\theta _1} = \sqrt n \sin {\theta _2}$$ then value of n is ________.