Question

A crane is used to lower weights into a lake for an underwater construction project. Determine the tension in the rope of the crane due to a 1m-diameter spherical steel block (density 88.005 g/cm3 ) when it is (a) suspended in the air and (b) completely immersed in water.

Please write Clearly

Answer 1

Solution

Volume of spherical block,

Mass of steel block,

Let tension in the rope be T.

Case 1: Suspended in air

Free Body Diagram

At equilibrium,

Therefore tension in the rope is 3.6163 MN.

Case 2: Immersed in water

Free Body Diagram

Let the buoyant force acting on sphere be F_b.

At equilibrium,

Therefore tension acting on the rope is 3.5752 MN.