A body of density 1.2 $$\times$$ 10³ kg/m³ is dropped from rest from a height 1 m into a liquid to density 2.4 $$\times$$ 10³ kg/m³. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is

Two solid spheres S₁ and S₂ of same uniform density fall from rest under gravity in a viscous medium and after sometime, reach terminal velocities v₁ and v₂, respectively. If ratio of masses $${{{m_1}} \over {{m_2}}} = 8$$, then $${{{v_1}} \over {{v_2}}}$$ will be equal to

Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is p, then surface tension of the bubbles is

A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm² hang from a ceiling and are 15 cm apart. Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar, so that each of the wires extends in length by 0.1 cm. At what distance from the steel wire, the load must be applied?

[Young's modulus of steel = 2 $$ \times $$ 10¹² dyne/cm² and that of brass = 1 $$ \times $$ 10¹² dyne/cm²]