Question

A system of masses rotating in different parallel planes is in dynamic balance if the resultant:

• A. Force is equal to zero
• B. Couple is equal to zero
• C. Force and the resultant couple are both equal to zero
• D. Force is numerically equal to the resultant couple, but neither of them need necessarily be zero

Hint:

For dynamic balance in rotating systems, both the resultant force and the resultant couple must be zero to ensure no net linear or rotational motion.

Answer 1

The Correct Option is C

For a system of rotating masses to be in dynamic balance, the resultant force and the resultant couple (torque) must both be zero. This ensures that there is no net linear force or rotational effect acting on the system.
- Force is equal to zero alone is not sufficient because a non-zero couple may still exist.
- Couple is equal to zero alone is not sufficient because a non-zero force may still be acting.
- Force and the resultant couple are both equal to zero is the correct condition for dynamic balance. If both the resultant force and the couple are zero, the system is in a state of dynamic equilibrium.
- Force is numerically equal to the resultant couple, but neither of them need necessarily be zero is incorrect because dynamic balance requires both to be zero.
Thus, dynamic balance is achieved when both the resultant force and couple are zero.