An insulating thin rod of length $$l$$ has a linear charge density $$\rho \left( x \right)$$ = $${\rho _0}{x \over l}$$ on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

A uniform metallic wire has a resistance of 18 $$\Omega $$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -

The density of a material in SI units is 128 kg m^–3 . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is -

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms^–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - (g = 10 ms^–2)