Question

If the height of TV tower is increased by $21\%$, then the transmission range is enhanced by:

• A. $10\%$
• B. $5\%$
• C. $15\%$
• D. $25\%$
• E. $12\%$

Answer 1

The correct option is A $10\%$

Range $=\sqrt{2Rh}\Rightarrow$ Range $\propto \sqrt{h}$
here h increases to $1.21$h
$\therefore$ Enhancement range $\propto (1.21{)}^{\frac{1}{2}}=1.1$
$\therefore$ increase $=1.1-1=0.10$
$\therefore \%$ increase $=0.10\times 100=10\%$.