A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is $\_\_\_\_$ cm.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is $\_\_\_\_$ .

An insulated wire is wound so that it forms a flat coil with $N=200$ turns. The radius of the innermost turn is $r_1=3 \mathrm{~cm}$, and of the outermost turn $r_2=6 \mathrm{~cm}$. If 20 mA current flows in it then the magnetic moment will be $\alpha \times 10^{-2} \mathrm{~A} . \mathrm{m}^2$. The value of $\alpha$ is $\_\_\_\_$ .

Consider a circuit consisting of a capacitor $(20 \mu \mathrm{~F})$, resistor $(100 \Omega)$ and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is $10 \Omega$. The time constant of the circuit is $\alpha \times 10^{-3} \mathrm{~s}$. The value of $\alpha$ is $\_\_\_\_$