A galvanometer of resistance ' $G$ ' is shunted by resistance of 'S' ohm. To keep the main current in the circuit unchanged the resistance to be put in series with Galvanometer is

In an A.C. circuit, the potential difference ' $V$ ' and current 'I' are given respectively by $\mathrm{V}=100 \sin (100 \mathrm{t}) \mathrm{V}, \mathrm{I}=100 \sin \left(100 \mathrm{t}+\frac{\pi}{3}\right) \mathrm{mA}$ The power dissipated in the circuit will be [Given $\rightarrow \cos \frac{\pi}{3}=\frac{1}{2}$]

An annular ring has mass 10 kg and inner and outer radii are 10 m and 5 m respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. Increase in length of the segment of railway track is ' $x$ ' $\times 10^{-5} \mathrm{~m}$. The value of ' $x$ ' is $\left(\alpha_{\text {steel }}=\right.$ $\left.1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$