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Q.

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 will be

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a

23

b

23

c

23

d

32

answer is B.

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Detailed Solution

As time period of physical pendulum  T=2πImglcThus T1=2πmR2+mR2mgR=2π2Rg ,    T2=2πmR22+mR2mgR=2π3R2g​⇒T1T2=23
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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 will be