Question

Students run an experiment to determine the rotational inertia of a large spherically shaped object around its center. Through experimental data, the students determine that the mass of the object is distributed radially. They determine that the radius of the object as a function of its mass is given by the equation r = km², where k = 3.

Which of the following is a correct expression for the rotational inertia of the object?

(A) m3
(B) 1.8 m3
(C) 3.6 m3
(D) 6 m3
(E) 9 m3

Answer 1

Answer:

(C) $3.6m^{5}$

Explanation:

$r=km^2$ = $3m^2$

Since the object is a solid sphere, the equation for rotational inertia is:

$I = \frac{2}{5}mr^2$

$I=\frac{2}{5}m(3m^2)^2=\frac{2}{5}*9m^5=3.6m^5$

Answer 2

The correct option is (C) which is,

$I=3.6m^5$

Given-

The equation for the radius according to the experiment,

$r=km^{2}$

{here constant K=3}

By putting the value of k in the above equation we get,

$r=3m^{2}$

It is known that for a spherically shaped object the moment of inertia can be written as,

$I=\dfrac{2}{5} mr^{2}$

Put the value of radius in the above formula of Inertia we get,

$I=\dfrac{2}{5} m[3m^2]^{2}$

$I=\dfrac{2}{5} *9m^5$

$I=3.6m^5$

Hence, the correct option is (C) which is,

$I=3.6m^5$

For more about the moment of Inertia, follow the link below,

https://brainly.com/question/6953943?referrer=searchResults