Question

A block of weight Wis supported by three strings as
shown in figure. Which of the following relations is
true for tension in the strings? (Here T, T, and To
are the tension in the strings A, B and Crespectively)
2​

Answer 1

Answer:T1=T3

Explanation:by using Lamis theorem we can solve this question

Lamis theorem states that when a body is acted upon by 3 forces and stays in equilibrium then the anyone of the force divided by the sine of the opposite angle will be equal to another force divided by the sine of the angle opposite to it.

So

Angle between A, B is given as 135 and the opposite force is T3

Angle between C,A is 90 and the opposite force is T2

Angle between B,C is 360-(90+135)= 135

And the force is T1.

From this info it's clear that since the angles opposite to the forces are equal only in the case of T1 and T3 . We can conclude T1= T3

Answer 2

Answer:

Tension, T₁ = T₃

Explanation:

[Refer to the attached image 1 to visualize the case]

Given;-

           Angle, α = 135°

Tensions for respective strings are;-

                T₁ = A

                T₂ = B

                T₃ = C

[Refer to the attached image 2 for the free body diagram of the given case from point where all the strings A, B and C join]

Let ∅ denote α - 90°

Then; ∅= 135° - 90 = 45°

Since, the net force = 0 (in the given case)

So,             Σ Fx = 0

Then,         T₁ = T₂ cos∅

                  T₁ = T₂/ √2 _____(1)

Similarly,   Σ Fy = 0

Then,        T₃ = T₂ sin∅

                T₃ = T₂/ √2_____(2)

From (1) and (2), we obtain;-

                 T₁ = T₃

Hence, the tension T₁ = T₃.

Hope it helps! ;-))