The moment of inertia of a thin uniform circular disc about one o f its diameters is I . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is

Question

The moment of inertia of a thin uniform circular disc about one o f its diameters is I . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is (A) √2I (B) 2I (C) (I/2) (D) (I/√2)

Tardigrade Admin · Accepted Answer

Let the moment of inertia about an axis perpendicular to the circular surface and passing through its center be

I_{c}

.
Moment of inertia about one of its diameter is

I

i.e.

I_{x} = I_{y} = I

Using perpendicular axis theorem:

I_{z} = I_{x} + I_{y}

∴ I_{C} = I + I = 2 I

Q. The moment of inertia of a thin uniform circular disc about one o f its diameters is $I$ . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is

$2 I$

$2 I$

$\frac{I}{2}$

$\frac{I}{2}$

Let the moment of inertia about an axis perpendicular to the circular surface and passing through its center be $I_{c}$ .
Moment of inertia about one of its diameter is $I$ i.e. $I_{x} = I_{y} = I$
Using perpendicular axis theorem: $I_{z} = I_{x} + I_{y}$
$∴ I_{C} = I + I = 2 I$

Q. The moment of inertia of a thin uniform circular disc about one o f its diameters is I . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is

2​I

2I

2I​

2​I​

Let the moment of inertia about an axis perpendicular to the circular surface and passing through its center be Ic​. Moment of inertia about one of its diameter is I i.e. Ix​=Iy​=I Using perpendicular axis theorem: Iz​=Ix​+Iy​ ∴IC​=I+I=2I

Q. The moment of inertia of a thin uniform circular disc about one o f its diameters is $I$ . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is

$2 I$

$2 I$

$\frac{I}{2}$

$\frac{I}{2}$

Let the moment of inertia about an axis perpendicular to the circular surface and passing through its center be $I_{c}$ .
Moment of inertia about one of its diameter is $I$ i.e. $I_{x} = I_{y} = I$
Using perpendicular axis theorem: $I_{z} = I_{x} + I_{y}$
$∴ I_{C} = I + I = 2 I$