wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A thin uniform rod of mass m, length L, area of cross section A and young's modulus Y rotates at angular velocity 'ω' in a horizontal plane about a vertical axis passing through one of its ends, then

A
tension in rod at distance 'r' from the axis of rotation is mw2(L2r2)2L.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
elongation of rod is 23mw2L2AY.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
elongation of rod is mw2L23AY.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
elongation of small element of rod decreases linearly as we move away from axis.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C elongation of rod is mw2L23AY.


T=mw2[r+(Lr)2]=mL(Lr)w2(L+r2)

T=mw2(L2r2)2L


Y=TAdldrdl=TAYdr

Δl=dl=L0mw22L(L2r2)drAY

Δl=mw22LAY.23L3=mw2L23AY

Since tension does not decrease linearly with radius, elongation of small element also does not decrease linearly with radius.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Hooke's Law
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon