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Q.

The maximum angular velocity with which a thin rod can be rotated about an axis passing through its centre c and perpendicular to the length without causing rupture is 'ω'. Then what is the safe angular velocity with which the same rod can be rotated about an axis passing through one end and perpendicular to its length?

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a

ω2

b

ω8

c

ω2

d

ω4

answer is C.

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Detailed Solution

In the first case maximum stress is induced at the mid point C and this stress is given by σmax=m2ω2.l4A=Alρ2ω2l4A=18ρω2l2In the second case, let the angular velocity be ω1.σmax=ρAlω12l2A=12ρω12l2∴ 12ρω12l2=18ρω2l2⇒ ω1=ω2
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