Question

The pulley and string as shown in the figure are smooth and of negligible mass . for the system to remain in equilibirium position the angle should be

Answer 1

Answer:

Angle, ∅ = 45°

Explanation:

[Refer to the attached image to visualize the case]

Since, same tension (T) will act on all the lengths of the string, hence, string lengths of mass √2 m will be equal. Since, they are equal, we can equate them. Also, tension on equal masses m will be mg.

Now;-

Component of Tension will be;-

     T cos∅ + T cos∅ = √2 mg  (Resultant T represent by dotted string)

                2T cos∅ = √2 mg

            2 mg cos∅ = √2 mg  [since, for m, T= mg]

                      cos∅ = √2/ 2

                      cos∅ = 1/√2

                            ∅ = 45°

Hence, for the system to remain in equilibrium the angle should be 45°

Hope it helps! ;-))