If the telecast is to cover a range of $64 \mathrm{~km}$, the height of $\mathrm{TV}$ tower should be (Radius of earth, $\mathrm{R}=6400 \mathrm{Km}$ )
A. $100 \mathrm{~m}$
B. $140 \mathrm{~m}$
C. $320 \mathrm{~m}$
D. $280 \mathrm{~m}$
If the telecast is to cover a range of $64 \mathrm{~km}$, the height of $\mathrm{TV}$ tower should be (Radius of earth, $\mathrm{R}=6400 \mathrm{Km}$ )
A. $100 \mathrm{~m}$
B. $140 \mathrm{~m}$
C. $320 \mathrm{~m}$
D. $280 \mathrm{~m}$

Correct answer is C.

Here,

Range $=d=64 \mathrm{~km}$, height $=\mathrm{h}$ and radius of earth $=$ $r=6400 \mathrm{~km}$.
$\begin{array}{l}
\text { Now }, d=\sqrt{2 h R} \\
\Rightarrow h=\frac{d^{2}}{2 R}=\frac{64 \times 64}{2 \times 6400} \\
\Rightarrow h=0.32 \mathrm{~km}=320m
\end{array}$