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QJEEM20Ph3f40: JEE Main 2020 Physics - Class 11 JEEM20Ph3f40 Solution: A ring is hung on a nail. It can oscillate, without slipping or …

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T1 and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T2. The ratio T1T2{{{T_1}} \over {{T_2}}} will be :

Multiple Choice Options

  • A 23{2 \over {\sqrt 3 }}
  • B 23{{\sqrt 2 } \over 3}
  • C 23{2 \over 3}
  • D 32{3 \over {\sqrt 2 }}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 5th September Evening Slot Physics - Rotational Motion Question 121 English Explanation

Moment of inertia in case (i) is I1

Moment of inertia in case (ii) is I2

I1 = 2MR2

I2 = 12MR2{1 \over 2}M{R^2} + MR2 = 32MR2{3 \over 2}M{R^2}

T1 = 2πI1Mgd2\pi \sqrt {{{{I_1}} \over {Mgd}}}

and T2 = 2πI2Mgd2\pi \sqrt {{{{I_2}} \over {Mgd}}}

⇒\Rightarrow T1T2=I1I2{{{T_1}} \over {{T_2}}} = \sqrt {{{{I_1}} \over {{I_2}}}}

= 2MR232MR2\sqrt {{{2M{R^2}} \over {{3 \over 2}M{R^2}}}}

= 23{2 \over {\sqrt 3 }}

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