A body of mass 2 kg is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity ‘ g ’, the reading on the spring balance will be

Options

A. 2 kg
B. `(4xxg)kg`
C. `(2xxg)kg`
D. Zero

Answer

To solve the problem step by step, we will analyze the forces acting on the body when the lift is descending with an acceleration equal to the acceleration due to gravity (g).

### Step 1: Identify the forces acting on the mass
When the mass (m) is hanging in the lift, two main forces act on it:
1. The gravitational force (weight) acting downward, which is given by \( F_g = m \cdot g \).
2. The tension (T) in the spring balance acting upward.

### Step 2: Write down the values
Given:
- Mass of the body, \( m = 2 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

Calculating the weight:
\[ F_g = m \cdot g = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19.6 \, \text{N} \]

### Step 3: Analyze the motion of the lift
Since the lift is descending with an acceleration equal to \( g \), the effective acceleration acting on the mass is:
\[ a = g \]

### Step 4: Apply Newton's second law
In the frame of reference of the lift, we can apply Newton's second law. The net force acting on the mass can be expressed as:
\[ F_{\text{net}} = T - F_g \]
Since the lift is accelerating downwards with acceleration \( g \), we can set up the equation:
\[ F_{\text{net}} = -m \cdot g \]
This means:
\[ T - F_g = -m \cdot g \]

### Step 5: Substitute the known values
Substituting \( F_g \) and \( m \):
\[ T - 19.6 \, \text{N} = -2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \]
\[ T - 19.6 \, \text{N} = -19.6 \, \text{N} \]

### Step 6: Solve for Tension (T)
Rearranging the equation to find T:
\[ T = 19.6 \, \text{N} - 19.6 \, \text{N} = 0 \, \text{N} \]

### Conclusion
The reading on the spring balance will be \( 0 \, \text{N} \).