Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
If a rod of mass m is fixed at one end and a particle of mass m is attached to its other end then what is the minimum velocity required for the system to perform circular motion?
Why is moment of inertia of the rod taken without any influence of particle and, the Rotational energy and KE is initial energy in Energy conservation equation. why?
if rod is fixed about one end & it is rotated in verticle plane then , moment of inertia about that end will be sum of both of particle as well as rod ...
I = Imass + Irod
= mL2 + mL2/3 = 4mL2/3 ...............1
now from energy conservation
[PE + KE ]i = [PE + KE]f ..................2
your question is why we take only KE at initial moment ???see if we are taking lowest point as refrence for potential energy then at bottom most point PE will be 0 & at topmost point it will be 2mgL ...
now i m taking the point of refrence at H meter below the lowest point then , initial PE will be
2mgH + mgL/2 (rod + mass) & final PE will be 2mgH + mg7L/2 (rod + mass) ....
indivisually both values are different but when we put these values in
enrgy conservation equation then result is same always ...so take any point as refrence & there is no need to assume that
at lowest point potential energy is 0 ...
now from eq 2 ,
(2mgH + mgL/2) + (KE)i = (2mgH+7mgL/2) + (KE)f
(KE)f = 0 , at top so
(KE)i = 3mgL
now , KE = IW2/2 = 2mL2W2/3 so , (from eq 1)
2mL2 W2/3 = 3mgL
W = 3(g/2L)1/2
V = Wr
=WL/2 = (3/2) (gL/2)1/2 m/s
approve if u like my ans
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !