contestada

A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?

a) 7/5 I
b) 3/5 I
c) 2/5 I
d) 1/7 I
e.2/7 I

Respuesta :

Answer:

option E

Explanation:

given,

I is moment of inertia about an axis tangent to its surface.

moment of inertia about the center of mass

[tex]I_{CM} = \dfrac{2}{5}mR^2[/tex].....(1)

now, moment of inertia about tangent

[tex]I= \dfrac{2}{5}mR^2 + mR^2[/tex]

[tex]I= \dfrac{7}{5}mR^2[/tex]...........(2)

dividing equation (1)/(2)

[tex]\dfrac{I_{CM}}{I}= \dfrac{\dfrac{2}{5}mR^2}{\dfrac{7}{5}mR^2}[/tex]

[tex]\dfrac{I_{CM}}{I}=\dfrac{2}{7}[/tex]

[tex]I_{CM}=\dfrac{2}{7}I[/tex]

the correct answer is option E

Otras preguntas