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 -

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 -

A magnet of total magnetic moment 10^-2 $${\widehat i}$$ A-m² is placed in a time varying magnetic field, B$${\widehat i}$$ (cos $$\omega t$$) where B = 1 Tesla and $$\omega $$ = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is -

To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is $$\mu $$, the torque, applied by the machine on the mop is -