Weight:

$\overline{){\mathbf{w}}{\mathbf{=}}{\mathbf{\rho}}{\mathbf{V}}{\mathbf{g}}}$

**A.**

Weight, W_{b} = (5000)(60.0 × 10^{-6})(9.81) = 2.943 N

The weight W_{b} of the ball is 2.943 N.

A cylindrical beaker of height 0.100 m and negligible weight is filled to the brim with a fluid of density ρ = 890 kg/m^{3}. When the beaker is placed on a scale, its weight is measured to be 1.00 N.

A ball of density ρ_{b} = 5000 kg/m^{3} and volume V = 60.0 cm^{3} 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 = 9.81 m/s^{2}

A. What is the weight W_{b} of the ball? Express your answer numerically in newtons.

B. What is the reading W_{2} 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.

C. What is the force F_{r} 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). Calculate your answer from the quantities given in the problem and express it numerically in newtons.

D. The rod is now shortened and attached to the bottom of the beaker. The beaker is again filled with fluid, the ball is submerged and attached to the rod, and the beaker with fluid and the submerged ball is placed on the scale. What weight W_{3} does the scale now show? Express your answer numerically in newtons.

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