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 that is 10 m long and makes an angle of 30 degrees with the horizontal, we can follow these steps:

### Step 1: Identify the parameters
- Mass of the block (m) = 4 kg
- Length of the inclined plane (d) = 10 m
- Angle of inclination (θ) = 30 degrees
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Calculate the vertical height (h) gained by the block
The vertical height (h) can be calculated using the sine function:
\[ h = d \cdot \sin(θ) \]
Substituting the known values:
\[ h = 10 \cdot \sin(30^\circ) \]
Since \( \sin(30^\circ) = \frac{1}{2} \):
\[ h = 10 \cdot \frac{1}{2} = 5 \text{ m} \]

### Step 3: Calculate the change in potential energy (PE)
The change in potential energy (PE) when the block is raised to height h is given by:
\[ PE = m \cdot g \cdot h \]
Substituting the values:
\[ PE = 4 \cdot 9.8 \cdot 5 \]
Calculating this:
\[ PE = 4 \cdot 9.8 = 39.2 \]
\[ PE = 39.2 \cdot 5 = 196 \text{ J} \]

### Step 4: Conclusion
The work done by the person in pushing the block up the incline is equal to the change in potential energy, which is:
\[ \text{Work done} = 196 \text{ J} \]

### Final Answer
The work done is **196 Joules**.

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