The fundamental frequency of a periodic signal is the lowest frequency that is present in the signal. It is the frequency that determines the pitch of the sound.
In the given signal, $v(t)$, the fundamental frequency is $100$ rad/s. This can be found by looking at the lowest frequency sine wave in the signal, which is $\sin(100t)$. The frequency of this sine wave is $100$ rad/s.
The other sine waves in the signal have frequencies that are multiples of the fundamental frequency. For example, the frequency of $\cos(300t)$ is $300$ rad/s, which is $3$ times the fundamental frequency. The frequency of $\sin\left(500t+\frac{\pi}{4}\right)$ is $500$ rad/s, which is $5$ times the fundamental frequency.
Therefore, the fundamental frequency of the signal is $100$ rad/s.
The other options are incorrect because they are not the frequencies of any of the sine waves in the signal.