Answer:
the moment of inertia is 4.5 × 10⁻⁵ kg.m²
Explanation:
Given that;
point mass m = 0.005 g = ( 0.005 / 1000 ) = 5 × 10⁻⁶ kg
perpendicular distance r = 3m
We know that a point mass doesn't have a moment of inertia around its own axis but, but using the parallel axis theorem, a moment of inertia around a distant axis of rotation can be determined using;
[tex]I_{}[/tex] = mr²
so we substitute
[tex]I_{}[/tex] = (5 × 10⁻⁶ kg) × (3 m)²
[tex]I_{}[/tex] = (5 × 10⁻⁶ kg) × 9 m²
[tex]I_{}[/tex] = 4.5 × 10⁻⁵ kg.m²
Therefore; the moment of inertia is 4.5 × 10⁻⁵ kg.m²
The moment of inertia of given point mass is 4.5 × 10⁻⁵ kgm² at a perpendicular distance of 3 m.
The moment of inertia of given point mass can be determined by,
[tex]I = mr^2[/tex]
Where,
[tex]I[/tex]- moment of inertia
[tex]m[/tex]- mass = 0.005 g = ( 0.005 / 1000 ) = 5 × 10⁻⁶ kg
[tex]r[/tex] - perpendicular distance = 3 m
Put the values in the formula,
[tex]I = (5 \times 10^{-6}{\rm \ kg}) \times (3 {\rm \ m})^2\\\\I = 5 \times 10^{-6}{\rm \ kg} \times 9 {\rm \ m}\\\\I = 4.5 \times 10^{-5} kgm^2[/tex]
Therefore; the moment of inertia of given point mass is 4.5 × 10⁻⁵ kgm².
To know more about moment of inertia,
https://brainly.com/question/6953943
