Two spheres, one heavier and weighing12000 N and of diameter 1.2 m and the other lighter and weighing 4000 N, are tied with a rope and placed in seawater. The density of sea water is 1025 kg/m^3. It was found that the spheres floated vertically with the lighter sphere just under the water surface. Illustrate the problem before answering the following questions: (a) Determine the diameter of the lighter sphere in meters.  (b) Determine the tension in the rope in Newtons.

A 0.5-m diameter helium (Density of He = 0.18 kg/m3) balloon is attached by a rope to the bottom of a 10-m deep freshwater lake (Fig. 1). Given that the rope can sustain a maximum tensile force of 300 N, would it be able to secure the balloon? Please clearly illustrate your free-body diagram.

An average adult has a mass of 81 kg, knowing that the average human density is very close to that of fresh water (1,000 kg/m3), (a) Calculate the buoyant force exerted by fresh water on that person. (b) If this adult jumped in a tank filled with Glycerine (sg = 1.263) what will be the percentage of the submerged volume below the surface?

There are various methods that can be used to calculate the hydrostatic force on a submerged surface. Which of the following statements are correct? (i) (iii) The pressure prism method gives good understanding of the fundamentals but it can only be used for plane surface uniform in the spanwise direction. The parallel axis theorem can be used for surface not uniform in the spanwise direction such as a circular or triangular plane surfaces, but it is limited to simple geometry where the second moment of area can be easily defined. The elementary area method can be used for any 2 or 3 dimensional surface as long as the geometric unit normal vector is known at any point on the surface. (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the above The Eulerian frame of reference is commonly used in analyzing fluid problems instead of the Lagrangian frame of reference. The main differences between these 2 frames of reference are: (i) The steady motion in Lagrangian frame of…