In the previous question the tension in the string is

Options

A. `(5)/(8)N`
B. `(8)/(5)N`
C. `(50)/(8)N`
D. `(80)/(5)N`

Explanation

To find the tension in the string of a conical pendulum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Length of the string (L) = 1 meter
- Mass of the bob (m) = 100 kg
- The angle of inclination (θ) is given by cos(θ) = 5/8 (from the previous question).

2. **Understanding Forces Acting on the Bob**:
- The forces acting on the bob are:
- The gravitational force (weight) acting downwards, which is \( mg \).
- The tension (T) in the string, which can be resolved into two components:
- \( T \cos(\theta) \) acting vertically upward.
- \( T \sin(\theta) \) providing the centripetal force required for circular motion.

3. **Balancing the Vertical Forces**:
- Since the bob is in equilibrium vertically, we can write:
\[ T \cos(\theta) = mg \]

4. **Substituting Known Values**:
- We know \( m = 100 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \) (approximating gravitational acceleration).
- Thus, \( mg = 100 \times 10 = 1000 \, \text{N} \).

5. **Using the Value of cos(θ)**:
- Substitute \( \cos(\theta) = \frac{5}{8} \) into the equation:
\[ T \left(\frac{5}{8}\right) = 1000 \]

6. **Solving for Tension (T)**:
- Rearranging the equation gives:
\[ T = \frac{1000 \times 8}{5} \]
- Simplifying this:
\[ T = \frac{8000}{5} = 1600 \, \text{N} \]

### Final Answer:
The tension in the string is \( T = 1600 \, \text{N} \).

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