A) doubled
B) halved
C) quadrupled
D) kept unchanged
Correct Answer: A
Solution :
Area [A] covered by TV signal is given by \[A=\pi {{d}^{2}}\] where d is range given by \[d=\sqrt{2Rh}\] where R is radius of earth and h the height of antenna. \[\therefore \] \[A=\pi (2Rh)\] Given, \[{{A}_{1}}=A,\,\,\,\,\,{{A}_{2}}=2A\] \[\therefore \] \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{h}_{1}}}{{{h}_{2}}}\] \[\Rightarrow \] \[\frac{{{h}_{1}}}{{{h}_{2}}}=\frac{1}{2}\] \[\Rightarrow \] \[{{h}_{2}}=2{{h}_{1}}\] Hence, height of transmitting antenna will have to be doubled.
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