Question

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21%

• A. 10%
• B. 21%
• C. 11%
• D. 15%

Answer 1

The correct option is A 10%

We know that,

$d_T=\sqrt{2R{h}_T}$

Now, let the transmission of the tower before be $=dr$,

Range after the height decreased $={dr}_2$

Ratio $=\frac{{dT}_2}{{dT}_1}=\sqrt{\frac{2Rh{T}_2}{2Rh{T}_1}}=\sqrt{\frac{{hT}_2}{{hT}_1}}$

height increases $=21$%

Thus,

$\frac{121}{100}{hT}_1=h{T}_2$

$\frac{{dT}_2}{{dT}_1}=\sqrt{\frac{{121hT}_1}{{100hT}_1}}=1.1$

$d_{T_2}:d_{T_1}=11:10$

Percentage increase in height

$=\frac{d_{T_2}-d_{T_1}}{d_{T_1}}\times 100=\frac{11-10}{10}=100=10$%

$\therefore$ $\left[A\right]=10$% correct answer.