Use dimensional analysis to derive the relationship between the periodic time of small oscillations of a simple pendulum ‘T’ and the length of the pendulum ‘l’ and the acceleration of gravity ‘g’.

Air enters a compressor operating at steady state at 1.05 bar, 300 k, with a volumetric flow rate of 93 m3/min and exits at 12 bar, 400 k. heat transfer occurs at a rate of 15.5 kw from the compressor to its surroundings. assuming the ideal gas model for air neglecting kinetic potential energy effects, determine the power in put in kw.

Two steel balls, each of mass m, are welded to a light rod of length l and negligible mass and are initially at rest on a smooth horizontal surface. a horizontal force of magnitude f is suddenly applied to the rod as shown. determine (a) the instantaneous acceleration a of the mass center g and (b) the corresponding rate at which the angular velocity of the assembly about g is changing with time.

How many neutrons does element x if it’s atomic number is 28 and its mass number is 87