Question

A body is held immersed in a liquid. (i) Name the two forces acting on body and draw a diagram to show these forces. (ii) State how do the magnitudes of two forces mentioned in part (i) determine whether the body will float or sink in liquid when it is released. (iii) What is the net force on body if it (a) sinks, (b) floats?

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Answer

(i) The two forces that act on the body immersed in liquid are —

  1. The weight W of the body acts vertically downwards, through the centre of gravity G of the body. This force tends to sink the body.
  2. The upthrust FB of the liquid acting vertically upwards, through the centre of buoyancy B i.e., the centre of gravity of the displaced liquid. This force tends to make the body float.

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(ii) Depending upon whether the maximum upthrust F’B is less than, equal to or greater than the weight W, the body will either sink or float in the liquid.

  1. When W > F’B i.e., the weight of the body is greater than the weight of the displaced liquid then the body will sink.
  2. When W = F’B i.e., the weight of the body is equal to the weight of the displaced liquid then the body will float just below the surface of liquid.
  3. When W < F’B i.e., the weight of the body is less than the weight of the displaced liquid the body will float partially submerged in the liquid. Only that much portion of the body gets submerged by which the weight of displaced liquid becomes equal to the weight of the body.

(iii) The net force on the body if it sinks/floats is as follows:

  1. In the case when the body sinks, the net force acting on the body is the weight of the body itself.
  2. In the case when the body floats, the net force acting on the body is the upthrust due to the liquid.

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