Question

In the following figure the masses of the blocks A and B
are same and each equal to m. The tensions in the strings
OA and AB are T, and T, respectively. The system is in
equilibrium with a constant horizontal force mg on B. The
Tis
mg
(a) mg
(b) 2 mg
(c) 13 mg
(d) 5 mg

Answer 1

Hence proved that T1 =  √5 mg and T2 = √2 mg

Option (b) and (c) are correct

Explanation:

∑Fx=0

mg−T2sinθ2=0

mg=T2sinθ2  ...... (1)

∑Fy = 0

mg−T2cosθ2=0

mg=T2cosθ2 ...... (2)

Dividing equations (1) /(2)

1 = tanθ2

θ2 = 45°

T2 = mg / sin 45°

T2 =  √2 mg

T1sin θ1 = mg -----(3)

Now T1 cosθ1 =mg + ( √2mg )cos 45°

T1 cosθ1 = 2mg    ----(4)

Dividing 3 / 4

tanθ1 = 1/2

θ1 = 26.57°

T1 = mg / sin 26.57°

T1 = √5 mg

Hence proved that T1 =  √5 mg and T2 =  √2 mg