Question

Question:A solid iron sphere and a solid lead sphere of the same size are each suspended by strings and are submerged in a tank of water. (Note that the density of lead is greater than that of iron.) Which of the following statements are valid? (Choose all correct statements.) (a) The buoyant force on each is the same. (b) The buoyant force on the lead sphere is greater than the buoyant force on the iron sphere because lead has the greater density. (c) The tension in the string supporting the lead sphere is greater than the tension in the string supporting the iron sphere. (d) The buoyant force on the iron sphere is greater than the buoyant force on the lead sphere because lead displaces more water. (e) None of those statements is true.

Short answer

(a) The buoyant force on each is the same

(c) The tension in the string supporting the lead sphere is greater than the tension in the string supporting the iron sphere.

Step-by-step solution

Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

B = $\rho$_FluidgV_disp

Where V_dispthe volume of fluid is displaced and $\rho$_Fluidis the density of the fluid.

Find which of the following statements are valid

Asitismotionedinthequestionthat,A solid iron sphere and a solid lead sphere of the same size are each suspended by strings and are submerged in a tank of water.

Therefore,BytheArchimedes’s principle, we can see that the buoyant force on each is the same (option a)

Similarly, if we resolve the forces on both spheres we can write the equations as,

B = mg+T

Where B the buoyant force on the solid is sphere and mg is the weight of solid sphere andis tension in the string in upward direction.

From equation we can see that the buoyant force is directly proportional to Tension in the string. And hence the tension in the string supporting the lead sphere is greater than the tension in the string supporting the iron sphere.

Therefor option (a) and (c) are the correct answers for this question.