Question

The unit of acceleration due to gravity in Newtons (N) and kilograms (kg) is:

• A. \( \text{N kg}^{-1} \)
• B. \( \text{kg N}^{-1} \)
• C. Nkg
• D. \( \text{N}^{-1} \text{kg}^{-1} \)

Hint:

\( g = \frac{F}{m} \Rightarrow \text{unit of } g = \text{N/kg} \)

Answer 1

The Correct Option is A

To determine the correct unit of acceleration due to gravity in terms of Newtons (N) and kilograms (kg), let's analyze the relationship between force, mass, and acceleration.

1. Newton's Second Law:
According to Newton's second law of motion:

$ F = m \times a $
where:
- $F$ is the force in Newtons (N),
- $m$ is the mass in kilograms (kg),
- $a$ is the acceleration in meters per second squared (m/s²).

2. Solving for Acceleration:
We can rearrange the equation to solve for acceleration:

$ a = \frac{F}{m} $

3. Determining the Units:
From this equation, we can see that the units of acceleration are:

$ \text{Units of } a = \frac{\text{Units of } F}{\text{Units of } m} = \frac{\text{N}}{\text{kg}} = \text{N kg}^{-1} $

4. Conclusion:
Therefore, the correct unit for acceleration due to gravity when expressed in terms of Newtons and kilograms is $\text{N kg}^{-1}$.

Final Answer:
The correct unit is $\boxed{\text{N kg}^{-1}}$.