THE MOMENTUM OF INTERIA OF A UNIFORM CYLINDER OF LENGTH L AND RADIUS OF R ABOUT IT PERPENDICULAR BISECT IS L.WHAT IS RATIO L/R SUCH THAT IS MOMENTUM OF INTERIA IS MINIMUM?
Answer (1)
21st Dec, 2019
Hii,
The answer to this will be:-
I=ml^2/12+mR^2/4I=ml212+mR^2/4
or I=m4(l23+R2)I=m4(l23+R2) -------------(1)
Also m=πR^2lp
=> R^2=m/πlp
Put in equation (1)
For maxima & minima
dIdl=m/4(2l3−m/πl^2ρ)=0
=> 2l/3=m/πl^2ρ=>2l/3=πR^2lρ/πl^2ρ
or 2l/3=R^2/l
=> l^2/R^2=3/2
or l^2R= root3/2
Hope this helps
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