A thin prism with angle $5^{\circ}$ of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is $\_\_\_\_$ .

A wire of uniform resistance $\lambda \Omega / \mathrm{m}$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points $A$ and $B(\mathrm{AOB})$ as shown in figure. The equivalent resistance between points $A$ and $B$ is $\_\_\_\_$ $\Omega$.

Two blocks with masses 100 g and 200 g are attached to the ends of springs $A$ and $B$ as shown in figure. The energy stored in $A$ is $E$. The energy stored in $B$, when spring constants $k_A, k_B$ of $A$ and $B$, respectively satisfy the relation $4 k_A=3 k_B$, is :

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is $\_\_\_\_$ mm.

[Assume least count is 0.01 mm ]