What will be the required height of a T.V. tower which can cover the population of `60.3 lakhs ` if average population density around the tower is `1000 km^(-2)`. Radius of earth ` = 6.4 xx 10^(6) m`.

Answer

` 150 m`

Explanation

Here , population covered ` = 60.3 lacks`
` = 60.3 xx 10^(5)` population density , ` rho = 1000 km^(-2)`
` = 1000 xx ( 1000 m)^(-2) = 10^(-3) m^(-2)`
Population covered = population density `xx` area covered
`:. 60.3 xx 10^(5) = 10^(-3) xx 3.14 xx d^(2)`
or `d^(2) = ( 60.3 xx 10^(5))/( 3.14 xx 10^(-3)) = 1.92 xx 10^(9)`
Height of the T.V. tower ,
` h = (d^(2))/( 2 R) = ( 1.92 xx 10^(9))/(2 xx 6.4 xx 10^(6)) = 150 m`