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Q.

Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is  I=MR24+L212. If such a cylinder is to be made for a given mass of material, the ratio L/R for it to have minimum possible I is :

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a

32

b

23

c

23

d

32

answer is A.

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Detailed Solution

I=MR24+ML212​Volume =V=πR2L​⇒R2=VπL∴I=MV4πL+ML212​⇒dIdL=MV4π−1L2+M2L12For minima, dIdL=0​⇒πR2L4πL2=2L12​⇒RL2=23​⇒LR=32
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