Question

the moment of inertia of a hollow thin shell of mass m and radius r about its geometrical axis is​

Answer 1

Answer:

As it is hollow, so almost all the mass is at periphery. Hence total moment of inertia aboit geometrical axis will be -

$m {r}^{2}$

Where, m is tge total mass and r is radius

Answer 2

The moment of inertia of a hollow thin shell of mass m and radius r about its geometrical axis is $2/3 Mr^2$

Explanation:

• Moment of inertia dictates that when a mass strikes an equal mass at rest and sticks to it, the combination must move at half the velocity, because the product of mass and velocity must remain constant.

Consider a hollow sphere of radius $r$.

Consider a strip(ring shape) on this surface of angular width dθ.

The strip being at position  from horizon.

Mass of elemental strip dm= $m/4\pi r^2$×$2\pi rcos$×$rd0$

$i = 2/3Mr^2$

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