Questions: Given the formula F= ma where - F represents force, - m represents mass and has units of kilograms ( kg ), and - a represents acceleration and has units of meters per second squared (m/s^2) Select an appropriate measurement unit for force. (A) kg/s (B) kg * m/s^2 (C) kg * m^2/s^2 (D) kg * m/s

Solution Steps

The given formula is \( F = ma \), where:

• \( F \) is the force,
• \( m \) is the mass in kilograms (kg),
• \( a \) is the acceleration in meters per second squared \(\left(\frac{m}{s^2}\right)\).

To find the appropriate unit for force, we need to multiply the units of mass and acceleration:

• Mass (\( m \)) has units of kilograms (kg).
• Acceleration (\( a \)) has units of meters per second squared \(\left(\frac{m}{s^2}\right)\).

Multiplying the units of mass and acceleration: \[ \text{Units of } F = \text{kg} \times \frac{m}{s^2} = \frac{\text{kg} \cdot \text{m}}{s^2} \]

We compare the calculated unit \(\frac{\text{kg} \cdot \text{m}}{s^2}\) with the given options:

• (A) \(\frac{\mathrm{kg}}{\mathrm{s}}\)
• (B) \(\frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}^{2}}\)
• (C) \(\frac{\mathrm{kg} \cdot \mathrm{m}^{2}}{\mathrm{~s}^{2}}\)
• (D) \(\frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}\)

The correct match is option (B) \(\frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}^{2}}\).

Final Answer