Inside a horizontal moving box, an experimenter finds that when an object is placed on a smooth horizontal table and is released, it moves with an acceleration of `10ms^(-2)`, in this box. If 1-kg body is suspended with a light string. The tension in the string in equilibrium position. (w.r.t. experimenter) will be (take `g=10ms^(-2)`)

Options

A. `10ms^(-2)`
B. `10sqrt(2)ms^(-2)`
C. `20ms^(-2)`
D. Zero

Explanation

To solve the problem, we need to analyze the forces acting on the 1-kg body suspended by a light string inside the moving box.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Suspended Body:**
- The body experiences two main forces: the gravitational force acting downward and the tension in the string acting upward.
- The gravitational force (weight) can be calculated using the formula:
\[ F_g = m \cdot g \]
where \( m = 1 \, \text{kg} \) and \( g = 10 \, \text{m/s}^2 \).

2. **Calculate the Weight of the Body:**
\[ F_g = 1 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10 \, \text{N} \]

3. **Consider the Pseudo Force:**
- Since the box is accelerating horizontally with an acceleration \( a = 10 \, \text{m/s}^2 \), a pseudo force acts on the suspended body in the opposite direction of the box's acceleration.
- The pseudo force \( F_p \) can be calculated as:
\[ F_p = m \cdot a = 1 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10 \, \text{N} \]

4. **Set Up the Equation for Tension:**
- In the equilibrium position, the tension \( T \) in the string must balance both the gravitational force and the pseudo force. The forces can be represented in a right triangle where:
- One leg is the gravitational force (10 N downwards).
- The other leg is the pseudo force (10 N horizontally).
- Using Pythagoras theorem, the tension can be calculated as:
\[ T = \sqrt{F_g^2 + F_p^2} = \sqrt{(10 \, \text{N})^2 + (10 \, \text{N})^2} \]

5. **Calculate the Tension:**
\[ T = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \, \text{N} \]

### Final Answer:
The tension in the string in the equilibrium position with respect to the experimenter is \( 10\sqrt{2} \, \text{N} \).