A person pushes a block of mass 4 kg up a frictionless inclined plane 10 m long and that makes an angle of `30^@` with the horizontal . Then the work done is

Options

A. `33.5 J`
B. `-392 J`
C. `339.4 J`
D. `-196 J`

Answer

To solve the problem of calculating the work done by a person pushing a block of mass 4 kg up a frictionless inclined plane of length 10 m at an angle of 30 degrees with the horizontal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Block:**
The gravitational force acting on the block can be calculated using the formula:
\[ F_g = m \cdot g \]
where \( m = 4 \, \text{kg} \) (mass of the block) and \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

2. **Calculate the Weight of the Block:**
\[ F_g = 4 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 39.2 \, \text{N} \]

3. **Determine the Height Gained by the Block:**
The height \( h \) gained by the block when it is pushed up the incline can be calculated using the sine of the angle:
\[ h = L \cdot \sin(\theta) \]
where \( L = 10 \, \text{m} \) (length of the incline) and \( \theta = 30^\circ \).
\[ h = 10 \, \text{m} \cdot \sin(30^\circ) = 10 \, \text{m} \cdot 0.5 = 5 \, \text{m} \]

4. **Calculate the Work Done Against Gravity:**
The work done \( W \) against gravity when lifting the block to height \( h \) is given by:
\[ W = F_g \cdot h \]
Substituting the values:
\[ W = 39.2 \, \text{N} \cdot 5 \, \text{m} = 196 \, \text{J} \]

5. **Consider the Direction of Work Done:**
Since the work is done against the gravitational force, we take it as negative:
\[ W = -196 \, \text{J} \]

### Final Answer:
The work done by the person in pushing the block up the incline is:
\[ \boxed{-196 \, \text{J}} \]