The moment of inertia of a body rotating about a given axis is 6.0 kg m2 in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is 5 cm and the unit of mass is 10 g?

A
2.4x10³
B
2.4x10⁵
C
6.0 x 10³
D
6.0 x 10⁵

Solution:

The dimensions of moment of inertia are (ML² ). We have

n₁(u₁) = n₂(u₂)

or $n_{1} (M_{1} {L_{1}}^{2}) = n_{2} (M_{2} {L_{2}}^{2})$

$∴ n_{2} = \frac{n_{1} (M_{1} {L_{1}}^{2})}{(M_{2} {L_{2}}^{2})} = n_{1} (\frac{M_{1}}{M_{2}}) {(\frac{L_{1}}{L_{2}})}^{2}$

Given n₁ = 6.0, M₁ = 1 kg, L₁ = 1 m, M₂ = 10 g and L₂ = 5 cm. Therefore,

$n_{2} = 6.0 \times (\frac{1 k g}{10 g}) \times {(\frac{1 m}{5 c m})}^{2} = 6.0 \times (\frac{1000 g}{10 g}) \times {(\frac{100 c m}{5 c m})}^{2} = 6.0 \times 100 \times {(20)}^{2} = 2.4 \times 10^{5}$

The moment of inertia of a body rotating about a given axis is 6.0 kg m²in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is 5 cm and the unit of mass is 10 g?

Solution:

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