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 solve the problem of finding the tension in the string of a conical pendulum, we can follow these steps:

### Step 1: Understand the forces acting on the bob
In a conical pendulum, the forces acting on the bob are:
- The gravitational force (weight) acting downward, \( mg \)
- The tension \( T \) in the string acting along the string at an angle \( \theta \) to the vertical

### Step 2: Resolve the tension into components
The tension can be resolved into two components:
- The vertical component \( T \cos \theta \) which balances the weight of the bob
- The horizontal component \( T \sin \theta \) which provides the centripetal force necessary for circular motion

### Step 3: Set up the equations
From the balance of forces, we can write:
1. For vertical forces:
\[ T \cos \theta = mg \]
2. For horizontal forces (centripetal force):
\[ T \sin \theta = \frac{mv^2}{r} \]
where \( v \) is the linear speed of the bob and \( r \) is the radius of the circular path.

### Step 4: Substitute known values
Given:
- Mass \( m = 100 \) grams = \( 0.1 \) kg
- Gravitational acceleration \( g = 10 \, \text{m/s}^2 \)
- \( \cos \theta = \frac{5}{8} \)

Substituting into the first equation:
\[ T \cos \theta = mg \implies T \left(\frac{5}{8}\right) = 0.1 \times 10 \]
\[ T \left(\frac{5}{8}\right) = 1 \implies T = \frac{1 \times 8}{5} = \frac{8}{5} \, \text{N} \]

### Step 5: Conclusion
The tension in the string is:
\[ T = \frac{8}{5} \, \text{N} \]

### Final Answer
The correct option for the tension in the string is \( \frac{8}{5} \, \text{N} \).

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