Answer: the tension in the first string is 25N and the tension in the second string is 43.3N.
Step-by-step explanation:
T1
/\
/ \
/ \
/60° \
/ \
/ \
/_________\
O 5kg T2
30°
The present discussion considers the tensions T1 and T2 acting upon two strings, with a particle denoted as "O" possessing a mass of 5kg under scrutiny.
One may employ Newton's second law to calculate the magnitudes of the tensions present in a system, as it states that the overall force acting upon an object is proportional to the product of its mass and acceleration. In this instance, the particle remains at rest as the net force acting upon it is equal to zero. Henceforth, it follows that the equilibrium of tension in every string is contingent upon the equivocation of the weight of the particle along the corresponding string direction.
By means of trigonometry, it is feasible to ascertain the constituents of the particle's weight with respect to each directional axis.
weight = m * g = 5kg * 10m/s^2 = 50N
weight_x = weight * sin(30°) = 25N
weight_y = weight * sin(60°) = 43.3N