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Q.

A thin-walled tube of mass m and radius R has a rod of mass m and very small cross section soldered on its inner surface. The sideview of the arrangement is as shown

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The entire arrangement is placed on a rough horizontal surface. The system is given a small angular displacement from its equilibrium position, as a result, the system performs oscillations. The time period of resulting oscillations if the tube rolls without slipping is

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a

2π4Rg

b

2π2Rg

c

2πRg

d

None of these

answer is A.

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Detailed Solution

Rolling can be considered as pure rotation about point of contact, P: Now it is compound pendulum oscillating about ‘P’.

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T=2πImgd; where I=mR2+mR2=2mR2.

d=R/2

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