Consider Earth as a uniform sphere of diameter 12.7 $\times$ 10⁶ m,with a mass of the 5.98 $\times$ 10³⁰ kg,and a rotational period of 1 day.If Earth suddenly had a diameter of half this value without any loss of mass,calculate the new period of rotation. A)0.5 days B)2.0 days C)0.25 days D)4.0 days E)1.4 days

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere is given by I = 2/5 * M * R^2, where M is the mass and R is the radius of the sphere. If the radius is halved, the moment of inertia is reduced to 1/8 of its original value. Since angular momentum is conserved, the product of moment of inertia and angular velocity remains constant. Therefore, the new period of rotation can be calculated as T' = T * (I'/I), where T is the original period of rotation, I' is the new moment of inertia and I is the original moment of inertia. Substituting the values, we get T' = T * (1/8) = 0.25 days. Therefore, the answer is choice C.

Consider Earth as a Uniform Sphere of Diameter 12 ×\times× 106 M,with a Mass of the 5

Consider Earth as a Uniform Sphere of Diameter 12 $\times$ 10⁶ M,with a Mass of the 5