Calculating Work Expended

The question asks us to find the energy or work expended when a force acts on a mass causing displacement. Work done by a constant force is defined as the product of the force and the displacement in the direction of the force.

Given:

• Mass of the object = 150 g
• Force applied = 100 N
• Displacement of the object = 10 cm

To calculate the work done, we need to use the formula:

$\text{Work} = \text{Force} \times \text{Displacement}$

First, ensure all units are in the standard SI system. The force is already in Newtons (N), which is the SI unit for force. The displacement is given in centimeters (cm), which needs to be converted to meters (m).

Conversion of displacement:

$1 \text{ meter (m)} = 100 \text{ centimeters (cm)}$

So, $10 \text{ cm} = \frac{10}{100} \text{ m} = 0.1 \text{ m}$.

The mass (150 g) is given but is not needed for calculating the work done by a direct force causing displacement in the direction of the force. The work done depends only on the force applied and the distance moved in the direction of the force.

Now, substitute the values into the work formula:

$\text{Work} = \text{Force} \times \text{Displacement}$

$\text{Work} = 100 \text{ N} \times 0.1 \text{ m}$

Calculating the work:

$\text{Work} = 10 \text{ N} \cdot \text{m}$

The SI unit of work (and energy) is the Joule (J), where $1 \text{ J} = 1 \text{ N} \cdot \text{m}$.

So, the work expended is:

$\text{Work} = 10 \text{ J}$

Therefore, the energy or work expended is 10 J.

Let's compare this result with the given options:

• Option 1: 1000 J
• Option 2: 1 J
• Option 3: 10 J
• Option 4: 100 J

Our calculated value of 10 J matches Option 3.