Question

A body of volume 100 cm³ weighs 1 kgf in air. Find:

1. Its weight in water and
2. Its relative density.

Answer 1

Volume of body = 100 cm³

Weight in air, W₁ = 1 kgf = 1000 gf

Mass of body = 1 kg = 1000 g

R.D. of solid = 10

R.D. of water = 1

(i) Let  W₂ be the weight of the body in water.

R.D. of body = `W_1/(W_1 - W_2) xx "R.D. of water"`

or , 10 = `1000/((1000 - W_2)) xx 1`

or, 10(1000 - W₂) = 1000

or, 1000 - W₂ = 100

or, W₂ = 900 gf = 0.9 kgf

(ii) R.D. of body = Density in C.G.S. (without unit)

or, R.D. = `"Mass"/"Volume" = 1000/100 = 10`