A rock is suspended from a string, and it accelerates upward. Which statement is true concerning the tension in the string ?

Options

A. The tension points downward.
B. The tension is less than the weight of the rock.
C. The tension is equal to the weight of the rock.
D. The tension is greater than the weight of the rock.

Answer

To solve the problem regarding the tension in the string when a rock is suspended and accelerates upward, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Rock**:
- The rock experiences two main forces: the gravitational force (weight) acting downward, and the tension in the string acting upward.
- Let the mass of the rock be \( m \). Therefore, the weight of the rock is given by \( W = mg \), where \( g \) is the acceleration due to gravity.

2. **Draw a Free Body Diagram (FBD)**:
- In the FBD, represent the downward force (weight) as \( mg \) and the upward force (tension) as \( T \).
- The forces can be represented as:
- Downward: \( mg \)
- Upward: \( T \)

3. **Apply Newton's Second Law**:
- According to Newton's second law, the net force acting on the rock is equal to the mass of the rock multiplied by its acceleration (\( a \)).
- The net force can be expressed as:
\[ \text{Net Force} = T - mg \]
- Since the rock is accelerating upwards, the net force is also equal to \( ma \):
\[ T - mg = ma \]

4. **Solve for Tension (T)**:
- Rearranging the equation gives:
\[ T = mg + ma \]
- This shows that the tension in the string is equal to the weight of the rock plus the force required to accelerate it upwards.

5. **Analyze the Result**:
- The expression \( T = mg + ma \) indicates that the tension \( T \) is greater than the weight of the rock \( mg \) because it includes an additional term \( ma \) (the force due to the upward acceleration).
- Therefore, we conclude that the tension in the string is greater than the weight of the rock.

### Conclusion:
The correct statement concerning the tension in the string is that **the tension is greater than the weight of the rock**.