$(a)\;\sqrt 3 w_1 \\(b)\;\sqrt {\large\frac{3}{5}}w_1 \\ (c)\;\sqrt 2 w_1 \\ (d)\;w_1 $

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$v_{rms} =\sqrt {V_R^2+(V_L -V_L)^2}$

$\qquad= \sqrt {(30)^2+(40)^2}$

$\qquad= 50\;V$

Since at $w=w_2$ voltage accross the resistor is $50 V$ this must be resonance condition

$\therefore X_L=X_C$

$w_2L= \large\frac{1}{w_2C}$

$w_2= \large\frac{1}{\sqrt {LC}}$

also at $w=w_1$

$I= \large\frac{100}{X_L}$

$\quad= \large\frac{60}{X_L}$

$C= \large\frac{100}{w_1^2 L \times 60}=\frac{5}{3w_1^2L}$

$w_2=\large\frac{1}{\sqrt { L \times \Large\frac{5}{3 w_1^2 L}}}$

$\quad= \sqrt {\large\frac{3}{5}}$$w_1$

Hence b is the correct answer.

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