The power radiated by a linear antenna is proportional to the square of the current and the square of the antenna's length. Additionally, the radiated power depends inversely on the square of the wavelength of the electromagnetic wave. Thus, the proportionality relation is: \[ P \propto \left( \frac{l}{\lambda} \right)^2. \]
Final Answer: The power radiated from a linear antenna is proportional to: \[ \boxed{\left( \frac{l}{\lambda} \right)^2}. \]
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)
An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ____

Find the area of the region \[ R = \{(x, y) : xy \le 27,\; 1 \le y \le x^2 \}. \]
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______
