Understanding the Concepts
* Newton's Second Law: This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it's represented as: F = ma, where:
* F is the net force
* m is the mass
* a is the acceleration
Solving the Problem
1. Let's assign variables:
* Mass of body A: m_A
* Mass of body B: m_B = 3m_A (given that body B has three times the mass of body A)
* Force acting on both bodies: F
2. Apply Newton's Second Law to each body:
* Body A: F = m_A * a_A
* Body B: F = m_B * a_B
3. Since the force is the same for both bodies, we can set the equations equal to each other:
* m_A * a_A = m_B * a_B
4. Substitute m_B = 3m_A:
* m_A * a_A = (3m_A) * a_B
5. Simplify and solve for the ratio of accelerations:
* a_A = 3 * a_B
* a_B = (1/3) * a_A
Conclusion
The acceleration of body B is one-third the magnitude of the acceleration of body A.
