Answer to Question #142727 in Mechanics | Relativity for Sandra

Question

Two forces are acting on an object. Which of the following statements is correct? (a) The object is in equilibrium if the forces are equal in magnitude and opposite in direction. (b) The object is in equilibrium if the net torque on the object is zero. (c) The object is in equilibrium if the forces act at the same point on the object.
(d) The object is in equilibrium if the net force and the net torque on the object are both zero.

Answer 1

Explanations & Calculations

• For an object to be in equilibrium under the influence of 2 forces the conditions should be satisfied. Forces should be,

1) Equal in magnitude : if not a net force force is generated which breaks the equilibrium

2) Parallel & Opposite in direction : generation of a net force

3) In line : if not a torque is generated (even though (1) & (2) are okay) which breaks the equilibrium

Therefore,

(a) is incorrect as 'inline' is not described

(b) is incorrect as there could still be a net force which may breaks the equilibrium

$\qquad\qquad \small F_1r_1-F_2r_2 =0\to F_{net} =|F_1 - F_2|$

(c) is incorrect as the directions of the forces could still be acting in a manner which could break the equilibrium

(d) is correct as both the net force & the torque are zero.

Therefore, the answer is (d)