Question

76. A hoop of mass 500gm & radius 10cm is placed
on a nail, then the moment of inertia of the
hoop, when it is rotated about the nail will be-
- kgm?
1) 0.05 2) 0.02 3) 0.01 4) 0.03​

Answer 1

Answer:

Option (3) 0.01

Explanation:

If the radius of the hoop is r and mass m then the moment of inertia about its Centre of Gravity

$I_{CG}=mr^2$

Since the hoop is rotated about the nail i.e. it is rotated about the circumference edge

Therefore, by parallel axis theorem

The moment of inertia of the hoop is given by

$I=I_{CG}+mr^2$

$\implies I=mr^2+mr^2$

$\implies I=2mr^2$

Given m = 500 g = 0.5 kg

And r = 10 cm = 0.1 m

Therefore, the moment of inertia

$I=2\times 0.5\times 0.1^2$

$I=0.01$ kg-m²

Hope this helps.