Question

moment of inertia of a uniform disc about an axis through its centre is l1 and about an axis at a perpendicular distance d from its center is I2 . if m is mass of disc then which of the following is necessarily true.
l1=l2+md²
I2=I1+md²
I1+I2=md²
none of these​

Answer 1

Explanation:

I2=I1+md² is the answer ..

Answer 2

Answer:

The true statement is I₂=I₁+md².

Explanation:

We will solve this question through the concept of the parallel axis theorem. Which is given as,"if  "I" is the moment of inertia of an object about an axis through its center of mass and I' is the moment of inertia of about an axis passing through a distance d from its center and the mass of the object  is m, then the net moment of inertia is given as,

                   $I'=I+md^2$      (1)

Where,

I=moment of inertia of the object through its center

m=mass of the object

d=distance of the axis from the center of the object

I'=net moment inertia of the object through the axis

From the question we have,

I=I₁

I'=I₂

By substituting the values in equation (1) we get;

$I_2=I_1+md^2$        (2)

Hence, the true statement is I₂=I₁+md².

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