Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a potential $$V_1$$ and the other to $$V_2$$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to another end in 0.5 second. If $$x$$ and $$y$$ are in $$\mathrm{cm}$$ and $$t$$ in second, then the length of the string is

A body of density '$$\rho$$' is dropped from rest at a height '$$h$$' into a lake of density '$$\sigma' (\sigma>\rho)$$. The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces)