a thin rectangular magnet suspended freely has a period of oscillation equalto t . now it is broken into two equal halves and one piece is made to oscillate freely in the same field if its period of oscillation is T' the ratio T'/T is
This is a good level MCQ and is very important as it helps you boost your confidence and exposes you to a different variety of questions preparing yourself more for competitive entrance examinations like NEET, JEE, etc.
So coming to the question now, this is a question from Oscillations chapter connected with Rotational Motion, Magnetism and requires some knowledge of Projectile motion too.
As we know Time period for oscillating magnet is
T=2π* root of I/MB.........(1)
where I is the moment of inertia,
M is the magnetic moment
M=x×l
x=polestrength
When the magnet is broken in two equal parts, the new magnetic dipole moment is
M′=x×l/2=M/2
I′=ML^12\2
=M/2×L^2/2
=ML^2/12*8
=I/8
New time period is
T′=2π* root of I' / M′B
Putting all the values we get
T′/T=root of 1/4= 1/2
So the final answer is 1/2.
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