The length of the string of a simple pendulum is measured with a metre scale to be 90.0 cm.The radius of the bob plus thelength of the hook is calculated to be 2.13 cm using measurements with a slide callipers. What is the effective lengthof the pendulum? (The effective length is defined as the distance between the point of suspension and the centre of the bob.)

Explanation

To find the effective length of the pendulum, we need to consider both the length of the string and the distance from the point of suspension to the center of the bob. Here’s how to calculate it step by step:

### Step 1: Identify the Length of the String
The length of the string of the pendulum is given as:
\[ L_{\text{string}} = 90.0 \, \text{cm} \]

### Step 2: Identify the Radius of the Bob plus the Length of the Hook
The radius of the bob plus the length of the hook is given as:
\[ L_{\text{bob}} = 2.13 \, \text{cm} \]

### Step 3: Calculate the Effective Length
The effective length of the pendulum is the sum of the length of the string and the radius of the bob plus the length of the hook. Therefore, we can calculate the effective length as follows:
\[ L_{\text{effective}} = L_{\text{string}} + L_{\text{bob}} \]
Substituting the values:
\[ L_{\text{effective}} = 90.0 \, \text{cm} + 2.13 \, \text{cm} = 92.13 \, \text{cm} \]

### Step 4: Consider Significant Figures
Now, we need to express the final answer with the correct number of significant figures. The length of the string (90.0 cm) has three significant figures, while the radius of the bob (2.13 cm) has three significant figures as well. Therefore, we will round our final answer to three significant figures:
\[ L_{\text{effective}} = 92.1 \, \text{cm} \]

### Final Answer
The effective length of the pendulum is:
\[ \boxed{92.1 \, \text{cm}} \]

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