A ball of mass m b and volume V is lowered on a stringinto a fluid of density r

Question

A ball of mass mb and volume V is lowered on a stringinto a fluid of density r. Assume that the objectwould sink to the bottom if it were not supported by thestring.
What is the tension T in the string when theball is fully submerged but not touching the bottom?
Express your answer in terms of anyor all of the given quantities and g, the magnitude of theacceleration due to gravity. What is the tension T in the string when theball is fully submerged but not touching the bottom? Express your answer in terms of anyor all of the given quantities and g, the magnitude of theacceleration due to gravity.

Explanation / Answer

the forces working on the ball: gravitational force F=-m*g (m=mass of ball negative signbecause its working down) buoyant force B=V* (V-volume of ball) tension in the string T F+B+T=0 so we solve for T T=m*g-V* (always assuming that m/V is smaller than a.k.a. the ball is fully submerged)

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