Video Transcript
The moments 𝑀 one and 𝑀 two of two couples satisfy the equation 𝑀 one plus 𝑀 two is equal to zero. Which of the following is therefore true? Is it (A) the two couples are in equilibrium? (B) The two couples are not in equilibrium. (C) The two couples are equivalent to a force. Or (D) the two couples are equivalent.
We begin by recalling that a couple consists of parallel forces of equal magnitude acting in opposite directions. The sum of these forces must be zero. Hence, a couple cannot produce a net force. We can therefore eliminate the option that two couples are equivalent to a force, unless we mean a force of zero magnitude. If the couples are equivalent, as in option (D), it must be the case that 𝑀 one is equal to 𝑀 two. However, this can also be expressed as 𝑀 one minus 𝑀 two is equal to zero. And the question states that 𝑀 one plus 𝑀 two is equal to zero, which contradicts the stated condition for the equivalence of couples.
If the couples are in equilibrium, the counterclockwise moment due to the couples equals the clockwise moment due to the couples. This can be expressed as 𝑀 one is equal to negative 𝑀 two. Adding 𝑀 two to both sides, this can be rewritten as 𝑀 one plus 𝑀 two is equal to zero. And since this is stated in the question to be the case, we can conclude that the couples are in equilibrium. And the correct answer is option (A).
