What will be the minimum length of antenna required to transmit a radio signal of frequency 10 MHz?

The correct option is 7.5 m.

To transmit a signal effectively, the minimum length of a linear antenna (such as a quarter-wave monopole) needs to be one-quarter of the wavelength of the signal being transmitted. This relation is given by the formula:
$$L=\frac{\lambda }{4}$$
where L is the minimum length of the antenna and λ (lambda) is the wavelength of the radio signal.

First, we need to calculate the wavelength (λ) of the radio signal. The relationship between the speed of light (c), frequency (f), and wavelength (λ) is defined as:
$$\lambda =\frac{c}{f}$$

Given data:
• Speed of light in vacuum, $c=3\times {10}^8\text{m/s}$
• Frequency of the radio signal, $f=10\text{MHz}=10\times {10}^6\text{Hz}={10}^7\text{Hz}$

Substituting these values into the wavelength formula:
$$\lambda =\frac{3\times {10}^8}{{10}^7}=30\text{m}$$

Now, we calculate the minimum length of the antenna (L) using the quarter-wavelength relationship:
$$L=\frac{30}{4}=7.5\text{m}$$
Thus, the minimum length of the antenna required is 7.5 m.