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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Magnetic Properties of Matter

NTA Abhyas 2020 · Physics · Magnetic Properties of Matter

A magnetic needle of negligible breadth and thickness compared to...

A magnetic needle of negligible breadth and thickness compared to its length, oscillates in a horizontal plane with a period TT. The period of oscillation of each part obtained on breaking the magnet into nn& equal parts and perpendicular to the length is

Options

  1. ATT
  2. BTn\dfrac{T}{n}
  3. CnTnT
  4. D1n\dfrac{1}{n}

Correct answer

B. Tn\dfrac{T}{n}

Step-by-step solution

T = 2\pi\sqrt{\dfrac{I}{MB}}<br/><br/>onbreakingnequalpartsperpendiculartolength<br/><br/><br /><br />on breaking n equal parts perpendicular to length<br /><br />I′ = \dfrac{1}{12}\left(\dfrac{m}{n}\right){\left(\dfrac{l}{n}\right)}^{2} of each part

I′=In3,M′=MnI′ = \dfrac{I}{n^{3}}, M′ = \dfrac{M}{n}

T′T=I′M′×MI=1n3×n=1n⇒T′=Tn\dfrac{T^{′}}{T} = \sqrt{\dfrac{I^{′}}{M^{′}} \times \dfrac{M}{I}} = \sqrt{\dfrac{1}{n^{3}} \times n} = \dfrac{1}{n} ⇒ T^{′} = \dfrac{T}{n}
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