A stone of mass 20 g falling from height of 2 km hits the ground with a speed of `200 ms^-1`. The work done by the gravitational force is

Options

A. `100`J
B. `200`J
C. `300`J
D. `400`J

Answer

To find the work done by the gravitational force on a stone of mass 20 g falling from a height of 2 km, we can follow these steps:

### Step 1: Convert the mass and height to appropriate units
- The mass of the stone is given as 20 g. We need to convert this to kilograms:
\[ \text{Mass} = 20 \, \text{g} = \frac{20}{1000} \, \text{kg} = 0.02 \, \text{kg} \]
- The height is given as 2 km. We need to convert this to meters:
\[ \text{Height} = 2 \, \text{km} = 2 \times 1000 \, \text{m} = 2000 \, \text{m} \]

### Step 2: Calculate the gravitational force acting on the stone
- The gravitational force (weight) acting on the stone can be calculated using the formula:
\[ F = m \cdot g \]
where \( g \) (acceleration due to gravity) is approximately \( 10 \, \text{m/s}^2 \).
\[ F = 0.02 \, \text{kg} \times 10 \, \text{m/s}^2 = 0.2 \, \text{N} \]

### Step 3: Calculate the work done by the gravitational force
- The work done by the gravitational force can be calculated using the formula:
\[ W = F \cdot d \]
where \( d \) is the displacement (which is the height fallen, 2000 m).
- Since the force and displacement are in the same direction, we can simplify this to:
\[ W = F \cdot h \]
\[ W = 0.2 \, \text{N} \times 2000 \, \text{m} = 400 \, \text{J} \]

### Final Answer
The work done by the gravitational force is:
\[ \boxed{400 \, \text{J}} \]