question_answer

The maximum distance up to which TV transmission from a TV tower of height h can be received is proportional to:

A) \[{{M}_{e}}\]    

B)                       \[\therefore \]                 

C)       \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}}\]                       

D)       \[\Omega \]

Correct Answer: A

Solution :

Let height of TV antenna be h and radius of earth is R and R >> h.                    Let M be receiving station when h<<R then NM may be assumed as tangent to  the surface of earth, so     \[\Omega \] \[\Omega \]   \[\Omega \] \[\Omega \] \[\Omega \]  \[1:{{2}^{1/3}}\] \[{{2}^{1/3}}:1\] Since,     h << R So, \[2:1\] may be neglected hence, \[1:2\] \[{{m}^{-2}}{{s}^{-1}}\]  \[{{m}^{-2}}{{s}^{-1}}\]