The mass of a body measured by a physical balance in a lift at rest is found to be m . If the lift is going up with an acceleration a , its mass will be measured as

Options

A. `m(1-(a)/(g))`
B. `m(1+(a)/(g))`
C. `m`
D. Zero

Answer

To solve the problem, we need to understand how the measurement of mass changes when a body is in a lift that is accelerating upwards.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- When the lift is at rest, the mass of the body is measured as \( m \). This is the standard measurement where the only force acting on the body is the gravitational force, which is given by \( F_g = mg \), where \( g \) is the acceleration due to gravity.

**Hint**: Remember that the mass measured at rest is simply the weight divided by the gravitational acceleration.

2. **Considering the Lift's Acceleration**:
- When the lift accelerates upwards with an acceleration \( a \), a pseudo force acts on the body in the opposite direction of the acceleration. This pseudo force can be calculated as \( F_{pseudo} = ma \).

**Hint**: Pseudo forces are used in non-inertial frames to account for the acceleration of the frame itself.

3. **Net Force Acting on the Body**:
- In the accelerating lift, the total effective force acting downwards on the body is the sum of the gravitational force and the pseudo force:
\[ F_{net} = mg + ma = m(g + a) \]

**Hint**: The net force is the combination of all forces acting on the object in the accelerating frame.

4. **Understanding the Balance Measurement**:
- A physical balance measures the weight of the body, which is the net force acting on it. Therefore, the new effective weight of the body when the lift is accelerating upwards is:
\[ F_{new} = m(g + a) \]

**Hint**: The balance measures weight, which is the force due to gravity plus any additional forces from acceleration.

5. **Conclusion about Mass Measurement**:
- It is important to note that the mass of the body itself does not change; it remains \( m \). The balance will show a higher reading due to the increased effective weight, but the mass remains constant.

**Hint**: Mass is an intrinsic property of matter and does not change with the conditions of motion.

### Final Answer:
The mass of the body measured by the physical balance in the lift moving upwards with acceleration \( a \) will still be \( m \).