The work done in dragging a stone of mass `100 kg` up an inclined plane `1` in `100` through a distance of `10 m` is `("takeg" = 9.8 m//s^(2))`

Options

A. zero
B. `980 J`
C. `9800 J`
D. `98 J`

Explanation

To solve the problem of calculating the work done in dragging a stone of mass 100 kg up an inclined plane, we can follow these steps:

### Step 1: Understand the Inclined Plane
The inclined plane has a slope of 1 in 100. This means for every 100 meters horizontally, the height increases by 1 meter. Therefore, we can deduce that:
- Height (h) = 1 meter
- Base (b) = 100 meters

### Step 2: Determine the Angle of Inclination
Using the relationship of the inclined plane, we can find the angle \( \theta \) using the sine function:
\[ \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{1}{\sqrt{100^2 + 1^2}} \approx \frac{1}{100} \]
For small angles, \( \sin \theta \approx \theta \) in radians.

### Step 3: Calculate the Weight of the Stone
The weight \( W \) of the stone can be calculated using the formula:
\[ W = mg \]
Where:
- \( m = 100 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \)

Calculating the weight:
\[ W = 100 \times 9.8 = 980 \, \text{N} \]

### Step 4: Determine the Force Along the Incline
The force acting along the incline due to gravity is given by:
\[ F_{\text{gravity}} = mg \sin \theta \]
Using \( \sin \theta \approx \frac{1}{100} \):
\[ F_{\text{gravity}} = 980 \times \frac{1}{100} = 9.8 \, \text{N} \]

### Step 5: Calculate the Work Done
The work done \( W_d \) in dragging the stone up the incline can be calculated using the formula:
\[ W_d = F \cdot d \]
Where:
- \( F = F_{\text{gravity}} \)
- \( d = 10 \, \text{m} \)

Calculating the work done:
\[ W_d = 9.8 \times 10 = 98 \, \text{J} \]

### Final Answer
The work done in dragging the stone up the inclined plane is \( 98 \, \text{J} \).

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