So here we have the two cases and the weights W are suspended using the three cards A. BNC. And we need to determine the tension in each card here. So let's first draw the figure here representing all the forces acting on this object. So there is weight and there will be tension. So on this cards, see the tension he will be acting so on A. And B. Let us see the tension acting here on A Is T. one and on be it is T. two. So at this point he will be acting in the downward direction as well. So basically we break these forces along horizontal and vertical direction. So if you break this t to this angle will be 45 because these two are parallel here. So along this direction, we break T two will get t to costs 45 and here we will get he too sign 45. Similarly, we break the Stephen along horizontally left, we will get even Cast 30 and vertically up. We will get given sign 30. So here we get you see that P. Is equal to W. So this is the tension in card. See and attention in court. A and B can be figured out by taking the equilibrium at this point here, So T one cost 30 that will be route three by two. This is equal to T. Two times Cost 45 pitches one by route to. So we solve this, we simplify here and we get the one as Route to buy route three times T two, that's one question and now we see the equilibrium of forces along the vertical direction. So t. to sign 45, that will be teacher into one. by route to plus Stephen sign 30 that will be won by two. And this is equal to the tension in court, see that's the weight which we have figured out here. So this is the equation too. So we simplify it and then we will take that as equation too. So we get the one plus Route two times T. two would be equal to two times W. So this is the question two. So instead of the Stephen were put in the value of Stephen from Equation one. So we get Route to buy route three times T two Plus Route two times T two, that will be to W. And here we can salute from both the sides. So on the new on the right hand side will get through to 32 x 2-3, prostitute Is equal to Route two times W. So let's get this value of T. two in terms of W. Here as well. 32 into one plus one by route three, that's equal to route to W. So if we figure out The value of one Plus one x 2 three, this comes out to be 1.5 77. 32 is 1.577 dividing this route to W. So we divide this routes to it's 1.577. And we get T to us .9 Times W. And once we get institute which is the tension in card be We can figure out the one that's route to buy route three. Route To buy route three times to to So if you figure out the value of Route to buy route three And we multiply that with .9 we get here as 0.73 Science W. T. one is .73 times W. So this is the tension in car eight and Kathy now in the similar manner we explored this case be so in case we're observing the free body diagram of the subject there will be wait here and the tension in car seats that will be of course let's see.
And now we observed they killed them at this point. So and string B. R. Discard big tension is acting here that C. T. B. And T. Representing tension and tension in card. See that will be equal to W. And here the same approach we apply for this ta and TB. So we break the forces along horizontal and vertical directions. So this tension and card be When we break that we get TV costs 45 that's one by due to and T. V. Sign 45. That's one by two here as well add on a here Tension in a if we break this we get this angle is 30° because we complete the strangle this is 60, this is 90. So by angle some property we get this as 30 degrees. So we'll get ta cost 30. That is Th Times Route three x 2. And in the downward direction we get PA. Sign 30. That's Ta into one x 2. So we take the equilibrium of forces along vertical and Horizontal direction. So we get T8 times Route three x 2 is equal to TV Times one Bedroom 2. So again we get here, this gets canceled. And TBS Route three by Route two times Diego. That's equation one. Now we take the equilibrium of forces along vertical direction. So we get three times one by route to is equal to tension in car seat. That's W. Plus the component of tension and card A. That's ta into one by two. So here we put in the values of PB and this equation to solve. So putting the value here we get route three times route two times T. A. Into one. by route to physical to W plus T. A. Y. two. So this gives us route three, T. E. Is equal to two W Plus T. A. So ta would be equal to two W. Over Route 3 -1. So if we simplify this we're going to get here as 2.73 times W. Is equal to tension and card We take this tension cardi and put it in equation one to get this attention card be the T. V would be equal to Route three by Route two times Th that's 2.73 times w. So if we simplify this year, we get here As 3.35 W. This is the tension in court B.