Question

If a particle has mass of 20 kg moves with an acceleration of \(2.5 \text{ m/s}^2\), then the magnitude of force acting on the particle is (in \(\text{kg}\cdot\text{m/s}^2\)):

• A. \(25\)
• B. \(50\)
• C. \(75\)
• D. \(100\)

Hint:

Always ensure all parameters are in their baseline SI units (kg and m/s^2) before multiplying. Since the units are already standard here, a direct calculation gives the answer immediately.

Answer 1

The Correct Option is B

Concept: According to Newton's Second Law of Motion for an object with a constant mass, the net force (\(F\)) acting on a body is directly proportional to the product of its mass (\(m\)) and its linear acceleration (\(a\)): \[ F = ma \] The standard SI unit for force is the Newton (\(\text{N}\)), which is equivalent to \(\text{kg}\cdot\text{m/s}^2\).

Step 1: Identifying the parameters given in the problem statement.
The problem provides the following values:
• Mass of the moving particle, \(m = 20 \text{ kg}\)
• Acceleration of the particle, \(a = 2.5 \text{ m/s}^2\)

Step 2: Substituting the values into Newton's Second Law formula.
Using the equation: \[ F = ma \] Substitute the given numerical values: \[ F = 20 \times 2.5 \]

Step 3: Evaluating the final multiplication.
We can rewrite the decimal value 2.5 as a fraction to simplify the calculation: \[ 2.5 = \frac{5}{2} \] Now substitute this back into the multiplication step: \[ F = 20 \times \frac{5}{2} \] Dividing 20 by 2 gives 10: \[ F = 10 \times 5 = 50 \text{ kg}\cdot\text{m/s}^2 \] The magnitude of the force acting on the particle is 50, matching option (2).