In a Young double slit experiment, the wavelength of incident light is $6000 \mathop {\rm{A}}\limits^{\rm{o}}$, the separation between slits $S_1$ and $S_2$ is 5 cm and the distance between slits plane and screen is 50 cm , as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is $\_\_\_\_$ Å.

A block takes $t$ time to slide down a plane inclined at $45^{\circ}$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$. The value of $\alpha$ is $\_\_\_\_$ .

The de Broglie wavelength for an electron accelerated through the potential difference of $V_1$ volt is $\lambda_1$. When the potential difference is changed to $V_2$ volt, the associated de Broglie wavelength is increased by $50 \%$. If $\left(V_1 / V_2\right)=(9 / \alpha)$, then the value of $\alpha$ is $\_\_\_\_$。

A moving coil of galvanometer when shunted with $2 \Omega$ resistance gives a full scale deflection for a current of 500 mA . When a resistance of $470 \Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is $\_\_\_\_$ $\Omega$.