For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from its pole can best be represented by (u = v is the reference line) :

The value of the acceleration due to gravity is g₁ at a height h = $${R \over 2}$$ (R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio $$\left( {{d \over R}} \right)$$ equals :

An electrical power line, having a total resistance of 2 $$\Omega $$, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then :
(assume the remaining portion to be spherical).