The normal reaction on a body placed in a lift moving up with constant acceleration `2ms^(-1) ` is 120 N. Mass of the body is (Take `g = 10ms^(-2)`)

Options

A. 10 kg
B. 15 kg
C. 12 kg
D. 5 kg

Answer

To solve the problem, we need to analyze the forces acting on the body placed in the lift that is moving upwards with a constant acceleration.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Body:**
- The gravitational force acting downwards, which is given by \( mg \), where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.
- The normal force \( N \) acting upwards, which is given as 120 N.
- A pseudo force acting downwards due to the acceleration of the lift, which is given by \( ma \), where \( a \) is the acceleration of the lift.

2. **Write the Equation of Motion:**
- Since the lift is accelerating upwards, we can write the equation of motion as:
\[ N = mg + ma \]
- Here, \( N \) is the normal force, \( mg \) is the weight of the body, and \( ma \) is the pseudo force due to the lift's acceleration.

3. **Substitute the Known Values:**
- We know:
- \( N = 120 \, \text{N} \)
- \( g = 10 \, \text{m/s}^2 \)
- \( a = 2 \, \text{m/s}^2 \)
- Substituting these values into the equation:
\[ 120 = mg + ma \]
\[ 120 = mg + m(2) \]
\[ 120 = m(10 + 2) \]
\[ 120 = m(12) \]

4. **Solve for Mass \( m \):**
- Rearranging the equation to solve for \( m \):
\[ m = \frac{120}{12} \]
\[ m = 10 \, \text{kg} \]

5. **Conclusion:**
- The mass of the body is \( 10 \, \text{kg} \).

### Final Answer:
The mass of the body is \( 10 \, \text{kg} \).

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