Question

✔Density of wood is 0.5gm/cc in the CGS system of units. The corresponding value in MKS units is?
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Answer 1

Answer:

Density of wood in MKS units is 500 kg / m^3 .

Explanation:

Given,

Density of wood is 0.5 gm / cc.

We know,

MKS unit of density is kg / m^3.

Method 1

= > 0.5 gm / c^3

= > 0.5 gm x c^( - 3 )

= > 0.5 ( 1000 / 1000 gm ) x [ ( 100 / 100 ) c ]^( - 3 )

= > 0.5 ( 1 kg / 1000 ) x [ 1 m / 100 ]^( - 3 )

= > 0.5 x 1 / 1000 x 1 / 100^( - 3 ) x kg / m^3

= > 0.5 x 1 / 10^3 x 1 / 10^( - 6 ) x kg / m^3

= > 0.5 x 10^( - 3 ) x 10^( 6 ) x kg / m^3

= > 0.5 x 10^( 6 - 3 ) kg / m^3

= > 0.5 x 10^3 kg / m^3

= > 0.5 x 1000 kg / m^3

= > 500 kg / m^3

Hence density of wood in MKS units is 500 kg / m^3 .

Method 2

= > Dimension formula of density = [ M L${}^{-3}$ ]

Let the numeric coefficient be n${}_1$

Here, using the dimension analysis

$\implies n_{1}=0.5\bigg[ \dfrac{g}{kg} \bigg]\bigg[ \dfrac{ cm }{m}\bigg]^3 \\\\\\\implies n_{1}=0.5\bigg[ \dfrac{g}{1000g}\bigg]\bigg[\dfrac{cm}{100 cm}\bigg]^{-3}\\\\\\\implies n_{1}=0.5\bigg[\dfrac{1}{1000}\bigg]\bigg[ \dfrac{1}{100}\bigg]^{-3}\\\\\\\implies n_{1}=0.5\bigg[\dfrac{1}{10^3}\bigg]\bigg[\dfrac{1}{10^2}\bigg]^{-3}\\\\\\\implies n_{1}=0.5 \times 10^{6-3}$

= > 0.5 x 10^3 kg / m^3

= > 500 kg / m^3

Density of wood in MKS units is 500 kg / m^3 .

Answer 2

Explanation:

Density of wood is 0.5gm/cc in the CGS system of units, then the corresponding value in MKS units will be 0.5gm/cc is 0.5 × 10-3 kg/ (10-2)3 m3. So, that becomes 0.5 × 10-3+6 kg/ m3 =0.5 × 103 kg/ m3=500 kg/ m. Therefore corresponding value in MKS units will be 500 kg/ m3.