GATE EC 2025 Set 1 Q29 — Circuit Analysis

In the circuit below, $M_{1}$ is an ideal AC voltmeter and $M_{2}$ is an ideal AC ammeter. The source voltage (in Volts) is $v_{s}(t)=100 \cos (200 t)$.

What should be the value of the variable capacitor $C$ such that the RMS readings on $M_{1}$ and $M_{2}$ are $25 \: \mathrm{V}$ and $5 \: \mathrm{A}$, respectively?