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A horizongal rod fixed at one of its end...

A horizongal rod fixed at one of its ends has lengtht `l`, rigidly modulus `eta` and area of cross-sectional `A`. A bob of mass `m` hangs from the freee end of the rod by a light spring of stiffness constant `k`, Find the small displacement of the free end of the rod.

A

`(A eta)/(mgl)`

B

`(mgA)/(eta l)`

C

`(mgl)/(A eta)`

D

`(eta l)/(mgA)`

Text Solution

Verified by Experts

The correct Answer is:
C
The distance `y` fallen by the tip of the rod is given as: `y = phi l`,

where `phi = (F)/(A eta)`
Then `y = (Fl)/(A eta)`
Subsituing `F = mg` (for equilibrium of the hanging mass),
we have `y = (mgl)/(A eta)`
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