A metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own axis in such a way that each part of the ring moves with a speed v. Find the tension in the ring.
1this ques was asked by me nd answered by qwerty bhaiyaa already itss a HCV ques (example).............
http://targetiit.com/iit-jee-forum/posts/circular-motion-easy-doubtsss-13650.html
1i tell u the simplest way of finding tension
first of all calculate total force acting on all elements (scalar sum of all forces acting on particle , BUT NOT VECTOR SUM)
i.e \int \left|dF(x) \right|
i.e in this question it is \frac{mv^2}{r}
divide this by 2\Pi
by doing this u easily get answer
try this method (it is correct in 99.99% cases)
1example:
let a non conducting metal ring which has +Q charge (uniformly distributed on ring) & a another -Q charge is placed at ring's center
find tension in ring (radius= R)
solution:
TOTAL FORCE acting on ring is -\frac{kQ^2}{R^2}
divide it by 2\Pi
so tension in ring is \frac{kQ^2}{2\Pi R^2}
(sorry,assume +ve charge on center element in case of finding tension ...if -ve charge is assumed then there will be no tension but compressive stress )
1Harsh , is ur trick applicable only for circular rings or even other geometrical bodies?
1i only applied on rings (where uniform distribution)
in other cases divide force by solid angle
i.e in case of sphere divide by 4\Pi
( NOTE : uniform distribution is required i.e charge,mass etc. )
(uniform distribution provides equal magnitude of force on unit elements)
1in straight rode there is not equal force on unit elements
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
I REQUEST U TO APPLY THIS ONLY ON RINGS...[9][4]
