Gravitation : NCERT Exemplar

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 Q.1     (a) A cube of side 5 cm is immersed in water and then in saturated salt solution. In which case will it experience a greater buoyant force? If each side of the cube is reduced to 4 cm and then immersed in water, what will be the effect on the buoyant force experienced by the cube as compared to the first case? Give  reason for each case.
            (b) A ball weighing 4 kg of density 4000 kg ${m^{ - 3}}$ is completely immersed in water of density $10^3$ $kgm^{ - 3}$. Find the force of buoyancy on it.  (Given g = 10 m${s^{ - 2}}$)

Sol.        (a) The density of saturated salt solution is greater than water, so the cube will experience greater buoyant force in   it. 
               If the volume of cube is reduced, less water will be displaced hence buoyant force will decrease.

               (b)  Mass of ball = 4 kg
               Density = 4000 kg/${m^3}$
               $volume\,\,of\,ball = {{Mass} \over {Density}} = {4 \over {4000}}{m^3} = {1 \over {1000}}{m^3}$
               buoyant force  = volume of ball x density of water x g
               =  ${1 \over {1000}} \times 1000 \times 10 = 10\, N$