Question

A metal piece weighs 200 gf in air and 150 gf when completely immersed in

water.

(a) Calculate the relative density of the metal piece.

(b) How much will it weigh in a liquid of density 0.8g/3

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Answer 1

Answer:

a = 4

b = 199.8 gf

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

Answer 2

Answer:

a = 4

b = 199.8 gf

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