Question

The moment of inertia of a disc of mass m and radius r about a tangent lying in its plane is?

• A. $\frac{3}{2}m{r}^2$
• B. $\frac{5}{2}m{r}^2$
• C. $\frac{5}{4}m{r}^2$
• D. $2m{r}^2$

Answer 1

The correct option is A $\frac{3}{2}m{r}^2$

The moment of inertia of a disc about its diameter$=\frac{M{R}^2}{4}$

According to the perpendicular axis theorem moment of inertia is the

sum of the moments of inertia of two perpendicular axes through the same point in the plane of the object about an axis perpendicular to the plane.

Thus moment of inertia of the disc about its axis $=\frac{M{R}^2}{2}$

As per theorem of parallel axis the moment of inertia of a body about an axis parallel to an axis passing through the center of mass of that body is equal to the sum of the moment of inertia of the body about an axis passing through center of mass and product of mass and square of the distance between the two axes.

Moment of inertia about the tangent lying to the plane$=\frac{M{R}^2}{2}+M{R}^2=\frac{3M{R}^2}{2}$