A solid uniform sphere has a density of 3000 kg/m³when the radius is equal to 0.6 m.If the mass stayed the same but the radius tripled in size,what would the new moment of inertia be for the sphere? A)98.0 kg.m² B)879 kg.m² C)294 kg.m² D)196 kg.m² E)2650 kg.m²

Question

Quizplus · Accepted Answer

The moment of inertia of a uniform solid sphere is given by:
$I = \frac{2}{5}mr^2$
where m is the mass of the sphere and r is its radius.

Given that the density of the sphere is 3000 kg/m3 and its radius is 0.6 m, we can find its mass as:
$m = \frac{4}{3}\pi r^3\rho = \frac{4}{3}\pi(0.6^3)(3000) \approx 5428.2\ kg$

When the radius triples, it becomes 1.8 m. The new moment of inertia can be found using the same formula, but with the new radius:
$I' = \frac{2}{5}m(1.8)^2 = \frac{2}{5}(5428.2)(1.8)^2 \approx 879\ kg.m^2$

Therefore, the answer is B.

A Solid Uniform Sphere Has a Density of 3000 Kg/m3

A Solid Uniform Sphere Has a Density of 3000 Kg/m³