Question

two objects are placed in a tank of water (density of 1.0 g/ml). object a sinks, while object b floats. which of the following statements must be true? i. object a must be less dense than object b. ii. object a must be more dense than object b. iii. object b must be less dense than the water. 4 pts iii only ii only ii and iii i only

Explanation:

Step1: Recall buoyancy principle

An object sinks if its density $
ho_{object}>
ho_{fluid}$, and floats if $
ho_{object}<
ho_{fluid}$.

Step2: Analyze object A

Object A sinks in water. So $
ho_A > 1.0\ g/mL$.

Step3: Analyze object B

Object B floats in water. So $
ho_B<1.0\ g/mL$.

Step4: Evaluate statements

• Statement I: Since $

ho_A > 1.0\ g/mL$ and $
ho_B<1.0\ g/mL$, $
ho_A>
ho_B$, so statement I is false.

• Statement II: As $

ho_A > 1.0\ g/mL$ and $
ho_B<1.0\ g/mL$, $
ho_A>
ho_B$, statement II is true.

• Statement III: Since object B floats, $

ho_B<1.0\ g/mL$ (density of water), statement III is true.

Answer:

C. ii and iii