00:01
So here we have been given the wire, a, b, c, and this is hinged at this point c.
00:08
And the complete wire is in equilibrium here, and we need to figure out the length for which the wire stays in this manner as described here.
00:21
So here, the total moment about this point c would be zero.
00:26
The sum of moments would be zero.
00:27
So we need to figure out the moment because of each section.
00:30
So for that, we will need the masses because there is.
00:33
Is gravitational force which is acting on this wire.
00:38
So to compute the weight, we need the masses.
00:41
So as this wire is given to be uniform, so the mass density, that's mass per unit length.
00:48
Let's take it as lambda.
00:50
That is going to be m by l plus 140, not 140, m by l plus 80 plus this length can be computed.
01:03
So for now we will take the length here as ab only because this is the constant which will be eliminated from the expression here because the net moment should be zero.
01:16
So this is this will be the mass per unit length and the mass of the section cd that will be mass density times its length that is l.
01:29
Similarly the mass of cb that will be lambda times its length that is 80.
01:35
Mass of ab.
01:37
So first we will compute this angle here.
01:39
So this is given as 60.
01:41
So basically this also will be 60.
01:43
And this angle here will be the tan inverse of this 60 divided by 80.
01:51
So here taking the tan inverse, we get the angle as 37 degree approximately.
01:59
So this comes out to be 37 degree.
02:02
And once we get this 37 degree, we can figure out this length.
02:06
Of ab as well or we can use simply pythagoras theorem so it will be 100 millimeter if we just take the root of 80 square plus 60 square so that will be root of 6 ,400 plus 3 ,600 and this is going to be 100 millimeters so mass of the section ab that will be lambda times 100 and now because of the weight acting on cd in the downward direction, its torque or the moment will be l by two times its mass into acceleration due to gravity.
02:49
And this will be a clockwise moment.
02:51
So we'll first figure out all the clockwise moment and then the anticlockwise moment and then we're going to equate that...