Question

Convert 5g/cm3to the sl unit

Answer 1

Answer:

We're asked to convert 5 g/cm³ to S.I unit.

$\implies \Bigg[n_{1} u_{1} \Bigg]_{CGS \: unit}=\Bigg[ n_{2} u_{2}\Bigg]_{S.I \: unit}$

• n₁ and n₂ are numerical values.
• u₁ and u₂ are the units of same physical quantity in different system.

$\implies 5 \times \frac{g}{cm^{3} } = n_{2} \times \frac{kg}{ {m}^{3} }$

• 1 kg = 10³ g
• 1 m = 10² cm
• 1 m³ = (10²)³ cm³ = 10⁶ cm³

$\implies 5 \times \frac{g}{cm^{3} } = n_{2} \times \frac{ {10}^{3} g}{ ( {10}^{2})^{3} cm^{3} }$

$\implies 5 = n_{2} \times \frac{ {10}^{3} }{ ( {10}^{2})^{3} }$

$\implies 5 = n_{2} \times \frac{ {10}^{3} }{ {10}^{6}}$

$\implies n_{2} = 5\times \frac{ {10}^{6} }{ {10}^{3}}$

$\implies n_{2} = 5\times {10}^{6} \times {10}^{ - 3}$

$\implies\underline{\boxed{\red{ \bf n_{2} = 5\times {10}^{3} \: \frac{kg}{ {m}^{3} } }}}$