A solid weighs 32 gf in air and 28.8 gf in water. What is the relative density of the solid?

2 Answers
May 15, 2018

#10#

Explanation:

  • #"m ="# Mass of solid
  • #"V ="# Volume of solid
  • #"ρ"_"s" ="# Density of solid
  • #"ρ"_"w" ="# Density of water
  • #"g ="# Acceleration due to gravity
  • #"F"_"b" ="# Bouyant force (#"= V ρ"_"w" "g"#)

In air

#32\ "gf = mg = Vρ"_"s" "g" color(white)(...)[∵ "Mass = Volume × Density"]#

Let’s call this as equation (1)

In water

#"28.8 gf = mg - F"_"b"#

#"28.8 gf = 32 gf – F"_"b"#

#"F"_"b" = "3.2 gf"#

#"Vρ"_"w" "g = 3.2 gf"# ………(2)

Didvide equations (1) and (2)

#(cancel"V" ρ_"s" cancel"g")/(cancel"V" ρ_"w" cancel"g") = (32 cancel"gf")/(3.2 cancel"gf") = 10#

Relative density is
#"RD" = "Density of solid"/"Density of water" = (ρ_"s")/(ρ_"w") = 10#

May 15, 2018

#10#

Explanation:

Relative density can also be found by using the formula

#"RD" = "Weight in air"/"Loss of weight in water"#

#"RD" = "32 gf"/"32 gf – 28.8 gf" = 32/3.2 = cancel(32)/(cancel(32) × 0.1) = 10#