00:02
Hello and welcome to this video solution of numerate.
00:05
Here it's given that there is a small object of mass 0 .4 kgs.
00:10
That is moving on a frictionless horizontal table in a circular path of radius 2 .2 meters.
00:19
And the angular speed is given to be 9 .9 radians per second.
00:25
Now the object is attached to a spring of negligible mass that passes through a small hole in the table at the center of the circle.
00:34
Someone under the table begins to pull the string downwards to make the circle smaller.
00:40
Right.
00:41
So what we have is here let's say we have the table right and here you have the hole.
00:46
There is this mass that is rotating in this circle and this rope passes downwards right.
00:54
And it is pulled inward so that the length shortens and it will move with a different speed at this point right.
01:03
And it's given that if the string can tolerate a maximum tension of 119 newton.
01:09
Now what is the radius of this smallest possible circle on which the object can move right.
01:14
Now what you can do is you can start by equating the angular momentum right.
01:21
L1 will be equal to l2.
01:23
Now l1 will be i1 omega 1 that will be equal to i2 omega 2 right.
01:28
I is the moment of inertia.
01:30
So the initial moment of inertia will be mr1 square omega 1.
01:34
That will be mr2 square omega 2 right.
01:38
Masses can be cancelled.
01:41
And here r1 is given to be 2 .2 squared omega 1 is 9 .9...