A child pulls a toy car from a distance of 20 m on smooth and horizontal plane. The string held in child's hand makes an angle of `60^@` with horizontal surface. If the force applied by the child is 10 N. the work done by child in pulling the car is

Options

A. 10J
B. 25 J
C. 50 J
D. 100 J

Answer

To find the work done by the child in pulling the toy car, we can use the formula for work done:

\[ W = F \cdot d \cdot \cos(\theta) \]

where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the direction of displacement.

### Step-by-Step Solution:

1. **Identify the given values**:
- Force \( F = 10 \, \text{N} \)
- Displacement \( d = 20 \, \text{m} \)
- Angle \( \theta = 60^\circ \)

2. **Convert the angle to radians if necessary**:
- In this case, we can use degrees directly since the cosine function can take degrees as input.

3. **Calculate \( \cos(\theta) \)**:
\[ \cos(60^\circ) = \frac{1}{2} \]

4. **Substitute the values into the work formula**:
\[ W = 10 \, \text{N} \cdot 20 \, \text{m} \cdot \cos(60^\circ) \]

5. **Calculate the work done**:
\[ W = 10 \cdot 20 \cdot \frac{1}{2} \]
\[ W = 10 \cdot 10 = 100 \, \text{J} \]

### Final Answer:
The work done by the child in pulling the car is \( 100 \, \text{J} \).

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