Question

Moment of inertia: A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that _________ to I2.
A. greater than
B. less than
C. Equal
D. Non comparable

Answer 1

Answer:

B.Less than

Explanation:

We are given that

Mass of each object=m

Length of rod=r

$I_1$=Moment of inertia of the dumbbell shaped object with respect to an axis passing through the center of the rod and perpendicular to it.

$I_2$=Moment of inertia with respect to an axis passing through one of the masses.

$I_1=\frac{mr^2}{4}+\frac{mr^2}{4}$

$I_1=\frac{2mr^2}{4}=\frac{1}{2}mr^2$

$I_2=mr^2$

$I_2>I_1$

Hence, $I_1$ is less than $I_2$

B.Less than