thin uniform disc of radius 25 cm and mass 1 kg has a hole of radius 5cm in it . if the centre of the circular hole is at a distance of 10 cm from the centre of the disc .calculate the moment of inertia of the disc about an axis perpendicular to its plane and passing through the centre of the hole
Answers
thin uniform disc of radius 25 cm and mass 1 kg has a hole of radius 5cm in it . if the centre of the circular hole is at a distance of 10 cm from the centre of the disc .calculate the
Answer:
Let σ be the mass per unit area. σ=
π(a
2
−b
2
)
M
The MI of the disk about O' is I=I
large
−I
small
....(1)
where I
large
is the MI of the larger disc without hole and I
small
is the MI of the hole
I
large
=(σπa
2
)
2
a
2
+(σπa
2
)c
2
,,,,,(2) using parallel axis theorem where (σπa
2
)
2
a
2
is thr MI of the larger disc about cm O.
I
hole
=(σπb
2
)
2
b
2
.....(3)
Substituting (2) and (3) in eqn(1)
I=(σπa
2
)
2
a
2
+(σπa
2
)c
2
−(σπb
2
)
2
b
2
=
π(a
2
−b
2
)
M
2
(a
4
−b
4
+2a
2
c
2
)
=
2
M
[(a
2
+b
2
)+
a
2
−b
2
2a
2
c
2
]
Explanation:
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