Submerged Sphere in a Beaker

Submerged Sphere in a Beaker

A cylindrical beaker of height 0.100m and negligible weight is filled to the brim with a fluid of densityρ = 890kg/m3 . When the beaker is placed on a scale, its weight is measured to be 1.00N .(Figure 1)

A ball of density ρb = 5000kg/m3 and volumeV = 60.0cm3 is then submerged in the fluid, so that some of the fluid spills over the side of the beaker. The ball is held in place by a stiff rod of negligible volume and weight. Throughout the problem, assume the acceleration due to gravity is g = 9.81m/s2 

PART A

What is the weight Wb of the ball?

ANSWER = 2.94 N

PART B

What is the reading W2 of the scale when the ball is held in this submerged position? Assume that none of the water that spills over stays on the scale.

ANSWER = 1.00 N

PART C

What is the force Fr applied to the ball by the rod? Take upward forces to be positive (e.g., if the force on the ball is downward, your answer should be negative).

ANSWER = 2.42 N

PART D

What weight W3 does the scale now show?

ANSWER = 3.42 N