The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the stirng at this instant.

Explanation

To find the tension in the string of the pendulum at the lowest point, we can follow these steps:

### Step 1: Identify the forces acting on the bob
At the lowest point of the pendulum's swing, two forces act on the bob:
1. The gravitational force (weight) acting downward, \( F_g = mg \)
2. The tension in the string, \( T \), acting upward.

### Step 2: Calculate the gravitational force
Given:
- Mass of the bob, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \) (since 1 g = 0.001 kg)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

The gravitational force can be calculated as:
\[ F_g = mg = 0.1 \, \text{kg} \times 10 \, \text{m/s}^2 = 1 \, \text{N} \]

### Step 3: Calculate the centripetal force
At the lowest point, the bob is also undergoing circular motion. The centripetal force required to keep the bob moving in a circle is provided by the tension in the string minus the gravitational force:
\[ F_c = \frac{mv^2}{r} \]
where:
- \( v = 1.4 \, \text{m/s} \) (the speed of the bob)
- \( r = 1 \, \text{m} \) (the length of the pendulum)

Calculating the centripetal force:
\[ F_c = \frac{mv^2}{r} = \frac{0.1 \, \text{kg} \times (1.4 \, \text{m/s})^2}{1 \, \text{m}} = \frac{0.1 \times 1.96}{1} = 0.196 \, \text{N} \]

### Step 4: Write the equation for tension
At the lowest point, the tension in the string can be expressed as:
\[ T = F_g + F_c \]
Substituting the values we calculated:
\[ T = 1 \, \text{N} + 0.196 \, \text{N} = 1.196 \, \text{N} \]

### Step 5: Round the answer
The tension in the string at the lowest point is approximately:
\[ T \approx 1.2 \, \text{N} \]

### Final Answer
The tension in the string at this instant is approximately **1.2 N**.

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