A gardener pushes a lawn roller through a distance of 20 m. If he applies a force of 20 kg wt in a direction inclined at `60^(@)` to the ground , find the work

Options

A. 1960 J
B. 196 J
C. 1.96 J
D. 196 kJ

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert the weight into force
The gardener applies a force of 20 kg weight. To convert this into Newtons, we use the formula:
\[ \text{Force (F)} = \text{mass (m)} \times g \]
where \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

Calculating the force:
\[ F = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \]

### Step 2: Identify the angle and displacement
The angle between the direction of the force and the displacement is given as \( 60^\circ \). The displacement is given as:
\[ d = 20 \, \text{m} \]

### Step 3: Use the work done formula
The work done (W) is calculated using the formula:
\[ W = F \times d \times \cos(\theta) \]
where:
- \( F \) is the force,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the displacement.

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ W = 196 \, \text{N} \times 20 \, \text{m} \times \cos(60^\circ) \]

### Step 5: Calculate \( \cos(60^\circ) \)
We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]

### Step 6: Calculate the work done
Now substituting \( \cos(60^\circ) \) into the equation:
\[ W = 196 \, \text{N} \times 20 \, \text{m} \times \frac{1}{2} \]
\[ W = 196 \times 20 \times 0.5 \]
\[ W = 1960 \, \text{J} \]

### Final Answer
The work done by the gardener is:
\[ \boxed{1960 \, \text{J}} \]

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