Question

A wooden block floats in water, and a steel object is attached to the bottom of the block by a string as in Figure OQ14.3. If the block remains floating, which of the following statements are valid? (Choose all correct statements.) (a) The buoyant force on the steel object is equal to its weight. (b) The buoyant force on the block is equal to its weight. (c) The tension in the string is equal to the weight of the steel object. (d) The tension in the string is less than the weight of the steel object. (e) The buoyant force on the block is equal to the volume of water it displaces.

Short answer

(d) The tension in the string is less than the weight of the steel object.

(e) The buoyant force on the block is equal to the volume of water it displaces.

Step-by-step solution

Step 1: 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:

$B={\rho }_{Fluid}g{V}_{disp}$

Where $V_{disp}$is the volume of fluid is displaced and ${\rho }_{Fluid}$is the density of the fluid.

Find which of the following statements are valid

From the above diagram it is clearly seen that block is in equilibrium, so the net force on the block must be zero:

$B_{Up}=mg\downarrow +T......\left(1\right)$

Where, $B_{Up}$is the upward buoyant force, $mg\downarrow$indicates weight in downward direction and T is tension.

Similarly for the steel object,

$B_{Up}+T=mg\downarrow ......\left(2\right)$

From equation (1) and (2) it is clear that option (a) and (b) are false because they don’t take into account the tension forces.

(c) Is false because it doesn’t take into account the buoyant force.

(d) Is true because$T=mg\downarrow -B_{Up}$ from Eqn (2).

(e) Is just the application of Archimedes principle to the part of the block that is submerged.

Hence option (d) and (e) is the correct answer for this question.