A wooden block floats in water, and a steel object is attached to the bottom of the block by a string as in Figure OQ15.1. 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.
The statements which are valid.
Answer to Problem 1OQ
Option (d).
Explanation of Solution
Buoyant force is the upward force exerted by a fluid on any immersed object. The magnitude of the buoyant force on an object always equals the weight of the fluid displaced by the object. Since the buoyant force is exerted by the fluid, it is not determined by the properties of the object except the amount of fluid displaced by it.
The buoyant force on the steel object is not equal to its weight since there are other forces acting on it. Similarly, the buoyant force on the block is either not equal to its weight. The weight of the steel object is not balanced by the tension in the string so that the tension is less than the weight of the steel object.
Conclusion:
Since the tension in the string is less than the weight of the steel object, option (d) is correct.
Since the buoyant force on the steel object is not equal to its weight, option (a) is incorrect.
Since the buoyant force on the block is not equal to its weight, option (b) is incorrect.
Since the tension in the string is not equal to the weight of the steel object, option (c) is incorrect.
Since the buoyant force on the block is not equal to the volume of the water it displaces but the weight of the water it displaces, option (e) is incorrect.
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