AIEEE 2003 Physics Solved Paper

KEY CONCEPT : The time period of a rectangular magnet oscillating in earth's magnetic field is given by
T=2π√‌

I

µBH

where I= Moment of inertia of the rectangular magnet
µ= Magnetic moment
BH= Horizontal component of the earth's magnetic field
Case 1:T=2π√‌

I

µBH

where I=‌

1

12

Mℓ2
Case 2 : Magnet is cut into two identical pieces such that each piece has half the original length.

Then
T′=2π√‌

I′

µ′BH

where I′=‌

1

12

(‌

M

2

)(‌

ℓ

2

)2=‌

I

8

and µ′=‌

µ

2

‌∴‌

T′

T

=√‌

I′

µ′

×‌

µ

I

‌=√‌

I∕8

µ∕2

×‌

µ

I

‌=√‌

1

4

=‌

1

2