When two blocks connected by a spring move towards each other under mutual interaction,

Options

A. (a) Their velocities are equal and opposite
B. (b) Their accelerations are equal and opposite
C. (c) The forces acting on them are equal and opposite
D. (d) Their momenta are equal and opposite

Explanation

To solve the problem of two blocks connected by a spring moving towards each other under mutual interaction, we can analyze the situation step by step.

### Step 1: Understand the System
We have two blocks, let's call them Block A and Block B, connected by a spring. When they move towards each other, they are influenced by the spring force.

**Hint:** Visualize the blocks and the spring. Consider how the spring behaves when it is compressed or stretched.

### Step 2: Identify the Forces
Since the blocks are connected by a spring, the force exerted by the spring on each block is equal in magnitude and opposite in direction (according to Newton's Third Law).

**Hint:** Remember that for every action, there is an equal and opposite reaction. This is crucial for understanding the forces acting on the blocks.

### Step 3: Analyze the Masses
Let’s denote the mass of Block A as \( m \) and the mass of Block B as \( 2m \). The forces acting on both blocks due to the spring will be equal, but since the masses are different, their accelerations will differ.

**Hint:** Use the formula \( F = ma \) to relate force, mass, and acceleration.

### Step 4: Calculate the Accelerations
Using Newton's Second Law, we can express the accelerations of both blocks:
- For Block A: \( a_A = \frac{F}{m} \)
- For Block B: \( a_B = \frac{F}{2m} \)

Since \( a_A \) and \( a_B \) depend on the mass, they will not be equal.

**Hint:** Compare the expressions for acceleration. Notice how the mass affects the acceleration.

### Step 5: Evaluate the Velocities
Since the blocks have different masses and experience the same force, their velocities will also differ. The relationship between force, mass, and acceleration implies that their velocities cannot be equal.

**Hint:** Remember that velocity is influenced by both acceleration and time. Different accelerations will lead to different velocities over time.

### Step 6: Analyze the Momentums
Momentum is given by the product of mass and velocity. Since the velocities of the blocks are different due to their different masses and accelerations, their momenta will also not be equal.

**Hint:** Use the formula for momentum \( p = mv \) to understand how mass and velocity contribute to momentum.

### Conclusion
From the analysis, we conclude:
- The forces acting on the blocks are equal and opposite (correct).
- Their accelerations are not equal (incorrect).
- Their velocities are not equal (incorrect).
- Their momenta are not equal (incorrect).

Thus, the correct answer is that the forces acting upon them are equal and opposite.

**Final Answer:** Option C: The forces acting upon them are equal and opposite.