A cylinder of mass 1 kg and radius 1 m is connected by two identical springs at a height of $$0.5m$$ above the center as shown in the Fig. The cylinder rolls without slipping. If the spring constant is $$30$$ $$kN/m$$ for each spring, find the natural frequency of the system for small oscillations.

When wet steam flows through a throttle valve and remains wet at exit

The specific heats of an ideal gas depend on its

Match List - $${\rm I}$$ with List - $${\rm II}$$

List - $${\rm I}$$
$$A.$$ Cetane number
$$B.$$ Approach and range
$$C.$$ $${\left( {{{\delta T} \over {\delta P}}} \right)_h} \ne 0$$
$$D.$$ $$dh = {c_p}\,\,dT,$$ even when pressure varies

List - $${\rm II}$$
$$1.$$ Ideal gas
$$2.$$ Vander Waals gas
$$3.$$ $$S.\,{\rm I}.$$ engine
$$4.$$ $$C.\,{\rm I}.$$ engine
$$5.$$ Cooling towers
$$6.$$ Heat exchangers