Consider a beaker filled partially with water sitting on a scale. The scale read

Question

Consider a beaker filled partially with water sitting on a scale. The scale reads wb, the total weight of the beaker and its water in air (Figure 1a). An object of mass m and volume V attached to a massless string is then lowered into the water until it is fully submerged (Figure 1b).

The scale now reads wb* > wb.        Figure 1a     Figure 1b

1. Show that the buoyant force B acting on the object is given by B = wb* wb.

2. Show that the volume V of the object is given by

V =(wb *wb) / g(water) where water is the density of the water and g is the acceleration of gravity.

Explanation / Answer

object of mass m will experience some upward force (buoyant force ) due to which its weight will reduce

but this buoyant force will be experienced by beaker in downward direction , increasing its weight

increase in weight of beaker = wb* wb = buoyant force

(water) * V * g =  wb* wb

V =  wb* wb /(g(water))

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