Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a bod

To calculate the acceleration due to gravity acting on a body on Earth, we can use the formula:

g = G * M / R^2

where:

• g is the acceleration due to gravity
• G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
• M is the mass of the Earth
• R is the radius of the Earth

Step 1: Determine the mass of the Earth (M) The mass of the Earth is approximately 5.972 × 10^24 kg.

Step 2: Determine the radius of the Earth (R) The radius of the Earth is approximately 6,371 km or 6,371,000 meters.

Step 3: Calculate the acceleration due to gravity (g) Using the formula g = G * M / R^2, we can substitute the values: g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (6,371,000 meters)^2

After performing the calculations, we find that the acceleration due to gravity on Earth is approximately 9.81 m/s^2.

Therefore, assuming the Earth to be a sphere of uniform density, the acceleration due to gravity acting on a body is approximately 9.81 m/s^2.