Wheatstone bridge principle is used to measure the specific resistance $$\left(S_1\right)$$ of given wire, having length $$L$$, radius $$r$$. If $$X$$ is the resistance of wire, then specific resistance is ; $$S_1=X\left(\frac{\pi r^2}{L}\right)$$. If the length of the wire gets doubled then the value of specific resistance will be :

A closed organ pipe $$150 \mathrm{~cm}$$ long gives 7 beats per second with an open organ pipe of length $$350 \mathrm{~cm}$$, both vibrating in fundamental mode. The velocity of sound is __________ $$\mathrm{m} / \mathrm{s}$$.

A series LCR circuit with $$\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}$$ and $$\mathrm{R}=10 \Omega$$, is connected across an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$ supply. The power factor of the circuit would be ________.

Two charges of $$-4 \mu \mathrm{C}$$ and $$+4 \mu \mathrm{C}$$ are placed at the points $$\mathrm{A}(1,0,4) \mathrm{m}$$ and $$\mathrm{B}(2,-1,5) \mathrm{m}$$ located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}$$. The magnitude of the torque acting on the dipole is $$8 \sqrt{\alpha} \times 10^{-5} \mathrm{Nm}$$, where $$\alpha=$$ _________.