Determine the tension in the string AD and reaction at C and B. The length of $AE = 750mm$

The value of $α $ can be determined from triangle ADC.

$ α = \tan^{-1}(DC/AC) = \tan^{-1}(100/500) = 11.31$

B is a contact force acting equally but in opposite directions on rod ABE and sphere D

Step 1: Isolated FBDs for rod and cylinder

Note: Since, Rb is the common reaction in both the FBD, it will act on both in opposite directions, as shown

Applying COE only on rod ADE

$∑M_A = 0 \\ Rb \times AB – 500 \times AE \cos (2α) = 0 \\ Rb \times 500 – 500 \times 750 \times \cos (22.62) = 0 ..... (AB = 500 \text { because triangles ABD and ACD are congruent and } AC= 500mm) \\ Rb = 692.3N \\ \text {Applying COE on cylinder } \\ ∑Fx = 0 \\ Rb \times \sin (2α) – T \times \cosα = 0 \\ T = 271.55 N \\ ∑Fy= 0 \\ -Rb \times \cos (2α) – T \sinα – W + Rc = 0 \\ W= 300N (given) \\ Rc = 992N↑$