The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by the following equation, where l is the length of the pendulum and g is acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. T=2π√l/g

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

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A2k pendulum has a speed of 1 m/s at a height of 1/2 meter