Water flows into a large tank with flat bottom at the rate of 10^–4m³s^–1. Water is also leaking out of a hole ofarea 1 cm² at its bottom. If the height of the water in the tank remains steady, then this height is -

In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle $${1 \over {40}}$$ by using light of wavelength $$\lambda $$₁. When the light of wavelength $$\lambda $$₂ is used a bright fringe is seen at the same angle in the same set up. Given that $$\lambda $$₁ and $$\lambda $$₂ are in visible range (380 nm to 740 nm), their values are -

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, 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 -