Question

(i)find lifting force of a 4 kg cork lifebelt in sea water if densities of cork and sea water are 0.2 *10^3 kg/m^3 and 1.03*10^3 kg/m^3
(ii)a crown made of gold and copper weighs 210 g in air and 198 g in water.The weight of gold in crown is (density of gold 19.3 g/cm^3 and density of copper is 8.5 g/cm^3
(iii)what will be heigth of liquid of density 3.4 g/cm^3 in barometer at a place where it is 70 cm of mercury barometer

Answer 1

1)  
         Volume of cork life belt = 4 kg / (200 kg/m³) = 0.02 m³
    if the entire volume of cork life belt is immersed in water, it will displace 0.02 m³ of sea water.  Then, the force of buoyancy will be

            0.02 m³ * 1030 kg/m³ * 9.81 m/sec²  = 202.086  Newtons

      Additional load it can carry (excluding its own weight )
                              =  202.086 N - 4 * 9.81 = 162.846 Newtons

2)
          wt in air = 210 gms = density  * volume
         wt in water = 198 gms => buoyancy force = 210-198 = 12 gms equivalent
            12 * g = Volume of crown * 1 gm/cm³ * g
             volume of crown = 12 cm³

    Let volume of Gold in Crown be x cm³.    volume of copper (12 - x) cm³
         weight of crown =  x * 19.3 + (12 - x) 8.5 =  210
                     x = 10 cm³   
       =>   weight of gold in crown = 19.3 * 10 = 193 gms

3)  

     Pressure is proportional to the height of the liquid column and density.
                 P = K * density * g * height
     As the pressure is same = atmospheric pressure, height is inversely proportional to the density.

                  height / 70  = 13.6 / 3.4
             =>               height = 280 cm