JEE Physics 2023 Question with Solution

Step-by-step solution

Common mistakes

• Using direct proportionality with $LC$ instead of inverse square-root dependence is incorrect. The resonant frequency varies as $\omega_0 \propto 1/\sqrt{LC}$, so increasing $L$ and $C$ decreases the frequency. Always apply the square root in the denominator.

• Multiplying the change factors incorrectly is a common error. Here, $L$ becomes $2L$ and $C$ becomes $8C$, so the product becomes $16LC$, not $10LC$. First combine the scaling factors correctly, then take the square root.

• Forgetting to compare the new frequency with the initial frequency leads to confusion about $x$. The question asks for the multiplicative factor relative to $\omega_0$, so rewrite the new result as a multiple of $\omega_0$ before choosing the option.