Question

The maximum distance between the transmitting and receiving TV towers is $D$. If the heights of both transmitting and receiving towers are doubled, then the maximum distance between them becomes

• A. $2D$
• B. $\sqrt{2}D$
• C. $4D$
• D. $D/2$

Answer 1

The correct option is B $\sqrt{2}D$

Distance between transmitting and receiving towers = $\sqrt{2h_{T}R}+\sqrt{2h_{R}R}=D$

Now, $h_T^{\prime }=2h_T$ and $h_R^{\prime }=2h_R$

Thus, $D^{\prime }=\sqrt{4h_{T}R}+\sqrt{4h_{R}R}=\sqrt{2}D$