Find the Gravitational Potential at a point on the earth’s surface. Take mass of earth as 5.98 X 10 24 kg, its radius as 6.38 X 10 6 m and G = 6.67 X 10 – 11 Nm2 kg – 2.
To find the gravitational potential at a point on the Earth's surface, we can use the gravitational potential formula:
V = -G * M / r
Where:
V is the gravitational potential,
G is the gravitational constant (6.67 x 10^(-11) Nm^2/kg^2),
M is the mass of the Earth (5.98 x 10^24 kg), and
r is the distance from the center of the Earth to the point on the surface (the radius, 6.38 x 10^6 m).
Plugging in the given values, we have:
V = - (6.67 x 10^(-11) Nm^2/kg^2) * (5.98 x 10^24 kg) / (6.38 x 10^6 m)
Calculating this expression will give us the gravitational potential at that point on the Earth's surface. Let's plug in the numbers and calculate.
To find the gravitational potential at a point on the Earth's surface, you can use the formula for gravitational potential:
Potential = G * (mass of object / distance from center of mass)
In this case, the mass of the object is the mass of the Earth, and the distance from the center of mass is the radius of the Earth. Plugging in the given values, we get:
Potential = (6.67 X 10^-11 Nm^2 kg^-2) * (5.98 X 10^24 kg) / (6.38 X 10^6 m)
First, we multiply the constants:
Potential = (6.67 X 5.98 X 10^24) / (6.38 X 10^6) * 10^(-11 - 24 + 6)
Next, we divide the numbers:
Potential = (3.98766 X 10^14) / (6.38 X 10^6)
To divide these numbers, we subtract the exponents:
Potential = 3.14137 X 10^8 Nm^-1
Therefore, the gravitational potential at a point on the Earth's surface is approximately 3.14137 X 10^8 Nm^-1.