When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration
due to gravity are 10³ kg m⁻³ , 0.07 Nm⁻¹ and 10 ms⁻² , respectively, the value of h (in mm) is _________.

A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm² and length $$\sqrt 3 $$ m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30$$^\circ $$ and 60$$^\circ $$, respectively. If elongation in copper wire is ($$\Delta {l_c}$$) and elongation in steel wire is ($$\Delta {l_s}$$), then the ratio $${{\Delta {l_c}} \over {\Delta {l_s}}}$$ is .............. .

[Young's modulus for copper and steel are 1 $$ \times $$ 10¹¹ N/m² and 2 $$ \times $$ 10¹¹ N/m² respectively.]

A liquid at 30$$^\circ $$C is poured very slowly into a Calorimeter that is at temperature of 110$$^\circ $$C. The boiling temperature of the liquid is 80$$^\circ $$C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50$$^\circ $$C. The ratio of the latent heat of the liquid to its specific heat will be ...........$$^\circ $$C.

[Neglect the heat exchange with surrounding]

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $${T_1} = 300\,K$$ and $${T_2} = 100\,K$$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller once and the thermal conductivities of the materials of the smaller and the larger cylinders are $${K_1}$$ and $${K_2}$$ respectively. If the temperature at the junction of the two cylinders in the steady state is $$200$$ $$K,$$ then $${K_1}/{K_2} = $$ ______________.