Question

Volume of a 500 g box is 450 cm cube. What is relative density of the material of the box and its weight in water?
Please give a detailed solution along with the answer....
a. 1.43, 100 g
b. 1.45, 50 g
c.1.11, 50 g

Answer 1

for he density of the box
d= m 
     v
   = 500
      450
d= 1.11
relative density = density of box       =     1.11   = 1.11 density
                           density of water            1
for the wight of box
m=W 
      g                 [g = 10 n/kg]
   = 500
       10
   = 50

Answer 2

mass of box = 500g
volume of box = 450 cm³

density = mass / volume
⇒ d = 500/450 g/cm³
⇒ d = 10/9 g/cm³
⇒ d = 1.11 g/cm³

relative density of a substance = density of substance / density of water
density of box = 1.11 g/cm³
density of water = 1 g/cm³

relative density of box = 1.11 / 1 = 1.11
(note that it has no unit)

If density of a substance is less than density of water, it will float on water and its weight in water will be 0. But density of box is higher than density of water. Since density of box is higher than density of water, it will submerge in water and it will have some weight in water.

weight of box in water =(density of box - density of water)×volume of box×g
⇒ weight in water = [(10/9) -1]×450×g
                           = [(10-9)/9]×450×g
                           = (1/9) ×450×g
                           = 50 g

So correct option is (c).