Question

1) mass of density bottle is 65 gram when filled with water its mass becomes 80 gram when filled with glycerine its mass becomes 105 gram. Calculate the density of glycerine
2) A piece of iron with mass 4.8 kg when dipped in a measuring cylinder raises the volume of water from 50 cm cube to 80 cm cube .Calculate the density of iron .


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Answer 1

Answers

(1) The density of glycerine is 2.666g/cm³

(2) The density of iron is 160g/cm³

Solutions :

(1) Given ,

the mass of the density bottle ,

m₁ = 65g

When it is filled with water its mass becomes 80g

so mass of water ,

m₂ = 80 - 65

⇒m₂ = 15g

We know that water has density of 1g/cm³

Again we know

$\sf \dashrightarrow \dfrac{Mass}{Volume} = density \\\\ \sf \implies \dfrac{15g}{V_{b}} = 1g {cm}^{-3} \: \: \: \{ Where \: V_{b} \: is \: the \: volume \: of \: the \: bottle \} \\\\ \sf \implies V_{b} = 15cm^{3}$

Now we are given that when the bottle is filled with glycerine its mass becomes 105g ,

Mass of glycerine is ,

m₃ = 105 - 65

⇒ m₃ = 40

Now density of glycerine ,

$\sf \implies d_{g} = \dfrac{m_{3}}{V_{b}} \\\\ \sf \implies d_{g} = \dfrac{40g}{15cm^{3}} \\\\ \sf \implies d_{g} = \dfrac{8}{3} gcm^{-3} \\\\ \sf\implies d_{g} = 2.666 gcm^{-3}$

Thus the density of glycerine is 2.666 g/cm³

__________________

(2) Given ,

Mass of iron ,

m = 4.8kg

⇒m = 4.8 × 1000 ᵍ

⇒ m = 4800g

Again when the piece of iron is dipped in a measuring cylinder of water it increases volume from 50cm³ to 80cm³

So, the volume occupied by the iron piece is

⇒V = (80 - 50)cm³

⇒V = 30cm³

Since We know that ,

$\sf \dashrightarrow Density = \dfrac{Mass}{Volume \: Occupied }\\\\ \sf \implies d_{i} = \dfrac{4800g}{30cm^{3}} \\\\ \sf \implies d_{i} = \dfrac{480}{3} gcm^{-3} \\\\ \sf \implies d_{i} = 160gcm^{-3}$

Thus density of iron is 160g/cm³

Answer 2

Answer:

1) Density of glycerine is 2.666 g/ cm ^3 .

2) Density of iron is 160 g/cm^3 .

Hope it helps you :--)