Question

The given system is in equilibrium. The block are at same horizontal level. The value of theta is :-


Diagram is in the atachment:- please help

Answer 1

see free body diagram,

for block of mass 2kg,

upward force = downward force

Tsinθ = 20N .....(1)

forward force = backward force

Tcosθ = N.....(2)

similarly for block of mass 4kg,

upward force = downward force

T'sin53° = 40N

or, T' × 4/5 = 40N

or, T' = 50N.....(3)

forward force = backward force

T'cos53° = N .....(4)

from equations (2) and (4),

Tcosθ = T'cos53°

or, Tcosθ = 50N × 3/5 [ from equation (3)]

or, Tcosθ = 30N .....(5)

now, from equations (1) and (5),

Tsinθ/Tcosθ = 20/30

or, tanθ = 2/3

or, θ = tan^-1(2/3)

hence, answer is θ = tan^-1(2/3)