When the temperature of a metal wire is increased from 0^oC to 10^oC, its length increases by 0.02%. The percentage change in its mass density will be closest to :

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of a wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be

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 ________.