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JEE Main Physics Class 12 Magnetism and Matter Questions
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Question : 76
Total: 80
The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be
[2004]
2
√
3
s
2
3
s
2
s
2
√
3
s
Validate
Solution:
Initially, time period of magnet
T
=
2
π
√
I
M
B
=
25
where
I
=
1
12
m
l
2
When the magnet is cut into three pieces the pole strength will remain the same and
Moment of inertia of each part,
(
I
′
)
=
1
12
(
m
3
)
(
l
3
)
×
3
=
I
9
We have, Magnetic moment
(
M
)
=
Pole strength
(
m
)
×
l
∴
New magnetic moment,
M
′
=
m
×
(
l
3
)
×
3
=
m
l
=
M
New time period,
T
=
2
π
√
I
′
M
′
B
=
2
π
√
I
9
M
B
⇒
T
′
=
T
√
9
=
2
3
s
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