The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

The moment of inertia of a thin uniform rod of mass M and length L abo

1.	The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
Answer» <html><body><p>`I_(0) +ML^(2)//2`<br/>`I_(0) + ML^(2)//4`<br/>`I_(0)+ <a href="https://interviewquestions.tuteehub.com/tag/2ml-1837952" style="font-weight:bold;" target="_blank" title="Click to know more about 2ML">2ML</a>^(2)`<br/>`I_(0) + ML^(2)`</p>Solution :According to the theorem of parallel axes , the moment of inertia of the <a href="https://interviewquestions.tuteehub.com/tag/thin-707663" style="font-weight:bold;" target="_blank" title="Click to know more about THIN">THIN</a> rod of <a href="https://interviewquestions.tuteehub.com/tag/mass-1088425" style="font-weight:bold;" target="_blank" title="Click to know more about MASS">MASS</a> M and length L about an axis passing through one of the ends is <br/> `I = I_(CM) + Md^2` <br/> where `I_(CM)` is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and d is the distance between <a href="https://interviewquestions.tuteehub.com/tag/two-714195" style="font-weight:bold;" target="_blank" title="Click to know more about TWO">TWO</a> parallel axes. <br/> Here `I_(CM) = I_(0) , d = (L)/(2) therefore I = I_(0) + M ((L)/(2))^(2) = I_(0) + (ML^(2))/(4)`</body></html>