Two circular coils of radius '$$a$$' and '$$2 a$$' are placed coaxially at a distance ' $$x$$ and '$$2 x$$' respectively from the origin along the $$\mathrm{X}$$-axis. If their planes are parallel to each other and perpendicular to the $$\mathrm{X}$$ - axis and both carry the same current in the same direction, then the ratio of the magnetic field induction at the origin due to the smaller coil to that of the bigger one is:
A metallic rod of $$2 \mathrm{~m}$$ length is rotated with a frequency $$100 \mathrm{~Hz}$$ about an axis passing through the centre of the circular ring of radius $$2 \mathrm{~m}$$. A constant magnetic field $$2 \mathrm{~T}$$ is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :
The power of a gun which fires 120 bullet per minute with a velocity $$120 \mathrm{~ms}^{-1}$$ is : (given the mass of each bullet is $$100 \mathrm{~g}$$)
The width of the fringes obtained in the Young's double slit experiment is $$2.6 \mathrm{~mm}$$ when light of wave length $$6000^{\circ} \mathrm{A}$$ is used. If the whole apparatus is immersed in a liquid of refractive index 1.3 the new fringe width will be :