A monochromatic light wave with wavelength $$\lambda_{1}$$ and frequency $$v_{1}$$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $$45^{\circ}$$ and $$30^{\circ}$$ respectively, then the wavelength $$\lambda_{2}$$ and frequency $$v_{2}$$ of the refracted wave are:

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $$\mathrm{W}$$ on earth will weigh on that planet:

A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $$\mathrm{K}_{1}$$ and $$\mathrm{K}_{2}$$. For the frictionless surface, the time period of oscillation of mass $$m$$ is :