Page 116 - Physics

Physics for Secondary Schools

lighter, for example, in salt water than in fl oating body, w . When an equilibrium is
B
fresh water and appears to weigh less in reached, these two forces balance. Hence,
water than in air. A ship fl oats more easily The upthrust in a liquid = weight of the
in the sea, and also it is easier to swim in
the ocean than in the lake because sea water liquid displaced.
is denser than lake water. Figure 5.9 shows
a marine vessel fl oating in seawater. U

w
B

Figure 5.10: A cork submerged in water

Figure 5.9: Ship vessel fl oating on a sea Consider a body of volume V and
For an object to fl oat on a fl uid the upthrust density ρ 1
1
exerted on it by the fl uid must be equal to Volume of submerged part is V
the weight of the object. That is, U = w. 2
Since, upthrust is equal to the weight of Weight of the body, w = V ρ g
B
1 1
the displaced fl uid, then, Upthrust of the fl uid U = V ρ g
Weight of the displaced liquid = 2 2
Apparent loss in weight of the object. From the principle of fl oatation;
Weight of a body = Upthrust of the fl uid
But,
apparent loss in weight = upthrust. V ρ g = V ρ g
2
1 1
2
and, V 1 = ρ 2
Upthrust = actual weight – apparent weight. V ρ
2 1
Since, volume of floating body density of liquid
upthrust = weight of the object. volumeof the submerged part of the object = density of body ⋅

Then, for an object to fl oat, its apparent = density of liquid ⋅
volume of floating body
volumeof the
weight must be zero. submerged part of the object density of body
Relationship between volume of Example 5.6
submerged part of the fl oating body
and the density of fl uid Suppose an 80 kg man fl oats in fresh
water with 92% of his volume submerged
Consider, a cork in Figure 5.10 submerged when his lungs are full of air. What is
in water of a particular volume and density. his average density? Take the density of
The two forces acting on a submerged water to be 1 000 kg/m .
3
body are upthrust U, and the weight of a

110
Student’s Book Form One

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