Calcualte the intensily of gravitational field due to a body of mass 20kg at a distance of 50cm from the body ?

Explanation

To calculate the intensity of the gravitational field due to a body of mass 20 kg at a distance of 50 cm, we will use the formula for gravitational field intensity (E) given by:

\[ E = \frac{GM}{R^2} \]

where:
- \(E\) is the gravitational field intensity,
- \(G\) is the universal gravitational constant, approximately \(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\),
- \(M\) is the mass of the body (20 kg in this case),
- \(R\) is the distance from the mass (50 cm, which we will convert to meters).

### Step 1: Convert the distance from cm to meters
Since the distance \(R\) is given in centimeters, we need to convert it to meters for consistency in units.

\[ R = 50 \, \text{cm} = \frac{50}{100} \, \text{m} = 0.5 \, \text{m} \]

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the gravitational field intensity formula.

\[ E = \frac{G \cdot M}{R^2} \]
\[ E = \frac{(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \cdot (20 \, \text{kg})}{(0.5 \, \text{m})^2} \]

### Step 3: Calculate \(R^2\)
Calculate \(R^2\):

\[ R^2 = (0.5 \, \text{m})^2 = 0.25 \, \text{m}^2 \]

### Step 4: Substitute \(R^2\) back into the equation
Now substitute \(R^2\) back into the equation for \(E\):

\[ E = \frac{(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \cdot (20 \, \text{kg})}{0.25 \, \text{m}^2} \]

### Step 5: Calculate the numerator
Calculate the numerator:

\[ 6.67 \times 10^{-11} \times 20 = 1.334 \times 10^{-10} \, \text{N m}^2/\text{kg} \]

### Step 6: Divide by \(R^2\)
Now divide the result by \(0.25 \, \text{m}^2\):

\[ E = \frac{1.334 \times 10^{-10}}{0.25} = 5.336 \times 10^{-10} \, \text{N/kg} \]

### Final Answer
Thus, the intensity of the gravitational field due to a body of mass 20 kg at a distance of 50 cm is:

\[ E \approx 5.34 \times 10^{-10} \, \text{N/kg} \]