Question

A metal weighs 50gf in air and 48 gf inside the water. What is the relative density of metal ?

Answer 1

Explanation:

• m = Mass of solid

• V = Volume of solid

• ρs= Density of solid

• ρw= Density of water

• g = Acceleration due to gravity

• Fb= Bouyant force (= V ρwg)

In air

200 gf = mg = Vρsg...[∵Mass = Volume × Density]

Let’s call this as equation (1)

In water

150 gf = mg - Fb

150 gf = 200 gf – Fb

Fb=50 gf

Vρwg = 50 gf ………(2)

Didvide equations (1) and (2)

Vρsg/Vρwg=200gf/50gf=4

Relative density is

RD=Density of solid/Density of water=ρs/ρw=10

First we use equation no 2 to find V;

Vpwg=50gf;

Density of water is 1000kg/m^3;

V=50/1000 f

= 1/20 f

Now calculating weight in another liquid of this solid;

Weight = 200gf – Vpg

Weight = 200gf – 1/20f(0.8g/3)g

= 200gf – 8/60fg

= 199.8 fg