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ne:, , , , , _ the volume of an equal, , State the assumption made in part (i), , (i) 140 cm? (ii) 140 gf (ii) 140 ef, Assumption : density of water = 1-0 ¢ om, , You are provided with a hollow iron ball A of volume, 15cm? and mass 12 g and a solid iron ballB of mass 12 g, Both are placed on the surface of water cance inl, large tub. (a) Find upthrust on each ball. (6) Which ball, will sink ? Give reason for your answer. (Density of abn, =§-0gcm~), (a) Upthrust on ball A = 12 gf and, on ball B = 1-5 gf. (b) The ball B will sink, , Reason : Volume of ball B = 12/8-0 = 1-5 cm?. Upthrust, on ball B is 1-5 gf which is less than its weight 12 gf,, while upthrust on ball A will be 15 ef if it is fully, submerged, w hich is greater than its w eight 12 gf, so it, will float with its that much part submerged for which, upthrust becomes equal to its weight (=12 ef)., A solid of density 5000 kg m 3 weighs 0-5 kgf im aur, It is completely immersed in water ol density, 1000 kg m™. Calculate the apparent weight of the solid, in water. 0-4 kgf, Two spheres A and B. each of volume 100 cm?, are placed on water (density = 1-08 em). The sphere A, is made of wood of density 0 3 gcm_ and the sphere B is, made of iron of density © 9gcm, (a) Find : (i) the w eight of each sphere, and (ii) the, upthrust on each sphere, (b) Which sphere will float ? Give reason, (a) (i) A - 30 gf, B- 890 af, GA ~ 30 gf, B- 100 st, (b) The sphere A will float, d is less than the, , Reason : The density of woo, density of water, , (B) RELATIVE DE, , 5.8 DENSITY, , t substances such, mercury €tc.,, we find that, f iron is much, , If equal volumes of different, as wood, iron, zinc, water, glycerine,, are weighed by a physical balance,, their masses are different. The mass ° or, More than the mass of a0 equal ed ee =, This is because the particles es os In other, more closely packed than those & ™ similar, , 4 5 han wood., Words, iron is denser tha otis 6d ted, , manner, if we take equal seca their volumes are, (say, one kg each), We notice that ! © ch larger than, different. The volume of cotton 1S mu, , mass of lead., , NSITY AND ITS MEASUREMENT BY, ARCHIMEDES’ PRINCIPLE, , This is because, , The mass of a block made of a certain material is, 13-5 kg and its volume is 15 x 10 3m?, (a) Calculate upthrust on the block if it is held fully, immersed in water., (b) Will the block float or sink in water W hen released ?, Give reason for your answer., (c) What will be the upthrust on block while floating?, Take density of water = 1000 kg m>, (a) 15 kgf. (b) The block will float since upthrust, on it when fully immersed in water, 1s more than its, weight. (c) While floating, upthrust = 13-5 kef., A piece of brass weighs 175 gf in air and 150 gf when, fully immersed in water. The density of water Is, 1:0 g cm’?. (i) What is the volume of the brass piece ?, (ii) Why does the brass piece weigh less in water ?, @) 25 cm?> (ii) due to upthrust., A metal cube of edge 5 cm and density 9-0 g cm> is, suspended by a thread so as to be completely immersed, in a liquid of density 12 g cm. Find the tension 10, thread. (Take g = 10m se), [Hint: Tension in thread = Apparent weight of the cube, in liquid] 9.75 N, A block of wood is floating on water with its, dimensions 50 cm xX 50 cm x 50 cm inside water., Calculate the buoyant force acting on the block. Take, g = 9-8 N kg bs ANS 1225 N, A body of mass 3.5 kg displaces 1000 cm? of water, when fully immersed inside it. Calculate : (i) the, volume of body, (ii) the upthrust on body and (iii) the, apparent weight of body in water., (i) 1000 cm? (ii) 1 kgf Git) 25 kef, , LE, , , , , , , , , , , the particles of lead are closely packed, while those, of cotton are very loose. In other words, lead is, denser than cotton. Thus to explain that equal, volumes of different substances have different, masses or equal masses of different substances have, different volumes, we use 4 term called density. It, is defined as follows : pees, | The density of a substance is its mass per unit, | volume. Lé., a, , } Density of a substance, aes Mass of the substance, , 2 Oe rn, = Volume of the substance, , pester, , i, , , , , , , , |, |, i, , eee, bo Sle OR, , er aa oe, , rs, pena), , a, anor, , per, , ae