The correct option is (a).
Explanation
Buoyancy is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. This phenomenon is governed by Archimedes' Principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.
Statement-wise Analysis:
- Statement 1 is Correct: Buoyancy (or upthrust) is defined as the upward force exerted by a fluid (liquid or gas) on an object immersed in it. This force arises due to the pressure difference in the fluid at different depths.
- Statement 2 is Incorrect: The magnitude of the buoyant force ($F_B$) is given by the formula $F_B = \rho V g$, where $\rho$ is the density of the fluid, $V$ is the volume of the displaced fluid, and $g$ is the acceleration due to gravity. Therefore, the buoyant force is directly proportional to the density of the fluid; it is not independent of it.
- Statement 3 is Incorrect: An object sinks if its weight (gravitational force acting downward) is greater than the buoyant force (upward force). If the buoyant force is greater than the object's weight, the object will rise to the surface and float. The statement incorrectly suggests the object sinks when the buoyant force is greater.
Key Takeaway:
Whether an object sinks or floats depends on the relationship between its weight and the buoyant force. An object sinks if its density is greater than that of the fluid (Weight > Buoyant Force) and floats if its density is less than that of the fluid.