Which, if either, of the basketballs in FIGURE Q5.16 are equilibrium? Explain.

Figure 5.16

here in question given the two figure of basketballs which feel the different forces on it and its asked as to explain which basketballs are in equilibrium and given the

explanation why the given basketballs are in equilibrium.

In the figure one basketball feel two forces and other one feel three forces

here the equilibrium means that when we do vector addition of the given system forces the net force is zero.

so by vector addition and newton's second law we can find the net force and decided the system is in equilibrium or not.

here we used Newton second law to find the which is

$F_{net}=ma$

where,

$F_{net}$is vector sum of all the forces acting on the object

$m$is mass of the object

$a$is acceleration of the object

now draw the free body diagram of the basketballs

here two forces acting on the basketball tension and gravitational which cancel the each other because of opposite direction of the forces.

so here we can say that by Newton`s second law if the object vector addition of the forces is zero then the object is called in the equilibrium.

there for this system is in equilibrium.

in above free body diagram shown that there are three forces applied to the basketball but when we take the vector addition of the above three forces then the net force is not zero so the system is not equilibrium

there for the system is not in equilibrium.