There is a small source of light at some depth below the surface of water (refractive index = $${4 \over 3}$$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) :
[Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2$$\pi $$rh]:

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then :

The current i in the network is :

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :