Question

6. A piece of wood of mass 150 g has a volume of
200 cm. Find the density of wood in
(a) C.G.S. unit, (b) S.I. unit.​

Answer 1

$\Large{\red{\underline{\underline{\tt{\blue{Given}}}}}}$

• Mass of wood = 150 g
• Volume of wood = 200cm³

$\Large{\red{\underline{\underline{\tt{\blue{To\:find}}}}}}$

• Density of wood in C.G.S unit and S.I unit

$\Large{\red{\underline{\underline{\tt{\blue{Solution}}}}}}$

Density in C.G.S unit

$\implies\sf Density=\dfrac{Mass}{Volume} \\ \\ \\ \implies\sf Density=\dfrac{150}{200} \\ \\ \\ \implies\sf Density=0.75g/cm^3$

__________________________

Density in S.I unit

• Mass of wood = 150/1000 = 0.15kg
• Volume of wood = 200/100 = 2m³
• Density = ?

$\implies\sf Density=\dfrac{Mass}{Volume} \\ \\ \\ \implies\sf Density=\dfrac{0.15}{2} \\ \\ \\ \implies\sf Density=0.075kg/m^3$

__________________________

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

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$\pink{\bf{Answer}\begin{cases}\sf{ \red{The\:Density\:of\:wood\:in\:C.G.S \:unit = }0.75 g/cm^3 \: }\\\sf{ \green{The\:Density\: of\: S.I.\: Unit = 0.075 kg/m^3.}\: }\end{cases}}$

$\pink{\bf{Given}\begin{cases}\sf{ \red{Mass\:of\:wood\:(M) = } 150\:gram\: }\\\sf{ \green{Volume\:of\:wood\:(V) = 200\:Cm^3}\: }\end{cases}}$

$\pink{\bf{Need\:To\:Find}\begin{cases}\sf{ \orange{The\:density\: of\:wood\:in\: :-} \: } \\\sf{ \red{C.G.S.\:Unit = \:} ? \: }\\\sf{ \green{S.I.\:Unit = \:?}\: }\end{cases}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

In case 1:

Given:

• A piece of wood of mass 150 g has a volume of 200 cm.

Need To Find:

• The density of wood in C.G.S. unit = ?

$\huge \underline \mathsf \red {Explanation:-}$

Formula used here:

• Density (D) = Mass/Volume

Putting the values according to the given formula:

➠ Density in C.G.S unit = 150/200

➠ Density in C.G.S unit = 0.75 g/cm³

Hence:

• The Density of wood in C.G.S unit is 0.75 g/cm³.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Now, In Case 2:

Given:

• Mass of wood = 150 gram

➠ 150/1000 = 0.15 kg

• Volume of wood = 200 Cm

➠ 200/100 = 2m²

Need To Find:

• Density of S.I Unit = ?

$\huge \underline \mathsf \red {Explanation:-}$

Formula used here:

• Density (D) = Mass/Volume

Putting the values according to the given formula:

➠ Density in S.I. Unit = 0.15/2

➠ Density in S.I. Unit = 0.075 kg/m³

Hence:

• The Density of S.I. Unit is 0.075 kg/m³.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$