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and the maximum upthrust on the body, ds will be F’, = VP,8- Following three, cases may arise :, , i) FW> Fs,, body will sink due to net, downwards., , W = Vopg, acting upwé, , or Vog > Vp;g Or P > PL the, force (W — F’,) acting, , fy ey For Vie = Virg OF P- p,, the, body will float and the net force on the body is, zero., , (iii) If W < F’, or Vog < Vp,g OF P < Pi» the, body will float due to net force (F’, — W) acting, upwards and only that much volume v of the body, will submerge inside the liquid due to which, upthrust F, (= vp,g) balances the weight W. The, net force on the body is zero in this situation also., , Thus a body of density p sinks in a liquid of, density p, if Pp > P,, while it floats if p = P, OF, p <p,. This can be demonstrated by the following, experiments., , Take an iron nail and a piece of cork, both of same mass. First place the iron nail on the, surface of water contained in a cup. The nail sinks., It implies that the force of gravity (or weight) on, iron nail pulling it downwards is greater than the, upthrust of water on the nail pushing it upwards., Now place the piece of cork on the surface of water., The cork floats. It means that upthrust on cork, when, fully immersed is more than that on nail because the, density of water is more than the density of cork,, , EXAMPLES, , Given : Weight of the body in air = 200 gf, Weight of the body in water = 190 gf, (i) Loss in weight of the body = 200 gf — 190 gf, = 10 gf, Upthrust on the body = loss in weight, = 10 ef., , (ui), , fo Ge re, ie, , , , , while the density of water is less than tha, nail., , Take few solid bodies of dj, materials of known density and place them . 9, surface of water. It is observed that if the dong A, the material of the body is equal to or |ey, 4, the density of water (i.e. P = Py 9 P< a, floats, implying that the upthrust on body dein, submerged part is equal to its own Weighty), F,= W). Different bodies float on water With 4, different volumes inside water. If p = 9, they.), floats with whole of its volume inside water, ‘ |, if p <p, the body floats with only that my!, volume inside water by which the upthrust F, body balances its weight W. On the other hang, the density of the material of body is more than i, density of water (i.e., P > p,,), the body Sinks,, because the upthrust due to water on body is ley,, than its weight (i.e., F, < W)., , Thus, bodies of density greater than that of the, liquid sink in tt, while bodies of average, density equal to or smaller than that of the, liquid float on tt. {, , An empty tin can (or iron ship) floats on wate, because its average density* is less than the density, of water., , , , F, =m49, B B, F,=mg, 9, s it falls |, orce due |, >» of stone |, , 108