What is the ratio of moment of inertia of a thin rod about an axis through mid-point and perpendicular to its length and that about an axis through one end and perpendicular to its length?

Question

What is the ratio of moment of inertia of a thin rod about an axis through mid-point and perpendicular to its length and that about an axis through one end and perpendicular to its length? (A)  (1/4)  (B)  (1/5)  (C)  (1/3)  (D)  (1/7)

Tardigrade Admin · Accepted Answer

MI of thin rod about an axis passing through mid-point is (ml2/12). Also, MI of thin rod about an axis passing through one of its end is (1/3)ml2. Now, required ratio =((1/12)ml2/(1)3ml2)=(1/4)

Q. What is the ratio of moment of inertia of a thin rod about an axis through mid-point and perpendicular to its length and that about an axis through one end and perpendicular to its length?

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{3}$

$\frac{1}{7}$

MI of thin rod about an axis passing through mid-point is $\frac{m l ^{2}}{12} .$ Also, MI of thin rod about an axis passing through one of its end is $\frac{1}{3} m l^{2} .$ Now, required ratio $= \frac{\frac{1}{12} m l ^{2}}{\frac{1}{3} m l ^{2}} = \frac{1}{4}$