Question

For a body to be in dynamic equilibrium, its:

• A. momentum should be zero
• B. acceleration should be zero
• C. kinetic energy should be zero
• D. velocity should be zero

Hint:

Remember that "dynamic" implies motion, and "equilibrium" implies zero net force. Zero net force always means zero acceleration, which in turn means constant velocity.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the condition required for a body to be in dynamic equilibrium.
Step 2: Detailed Explanation:
Equilibrium refers to a state where the net force acting on a body is zero.
There are two types of equilibrium:
1. Static Equilibrium: The body is at rest (velocity is zero).
2. Dynamic Equilibrium: The body is moving with a constant velocity.
According to Newton's Second Law of Motion, the net force \(F_{net}\) acting on a body is equal to the product of its mass (m) and acceleration (a), i.e., \(F_{net} = ma\).
For any type of equilibrium, the net force must be zero (\(F_{net} = 0\)).
Therefore, \(ma = 0\). Since the mass (m) of the body is non-zero, its acceleration (a) must be zero.
Let's analyze the given options:
(A) Momentum should be zero: Momentum (\(p = mv\)). In dynamic equilibrium, velocity (v) is constant but not zero, so momentum is also constant but not zero. This is incorrect.
(B) Acceleration should be zero: If acceleration is zero, the velocity is constant. This is the definition of dynamic equilibrium. This is correct.
(C) Kinetic energy should be zero: Kinetic energy (\(KE = \frac{1}{2}mv^2\)). In dynamic equilibrium, velocity (v) is non-zero, so kinetic energy is also non-zero. This is incorrect.
(D) Velocity should be zero: Zero velocity corresponds to static equilibrium, not dynamic equilibrium. This is incorrect.
Step 3: Final Answer:
The condition for a body to be in dynamic equilibrium is that its acceleration must be zero, which means it moves at a constant velocity.