The gravitational potential at a point above the surface of earth is −5.12×107 J/kg and the acceleration due to gravity at that point is 6.4 m/s2. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :
Question
The gravitational potential at a point above the surface of earth is −5.12×107 J/kg and the acceleration due to gravity at that point is 6.4 m/s2. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :
Solution
The gravitational potential energy (V) at a point in space due to Earth is given by the formula:
V = -GM/r
where: G is the gravitational constant (6.674 x 10^-11 N(m/kg)^2), M is the mass of the Earth (5.972 x 10^24 kg), r is the distance from the center of the Earth to the point in space.
The acceleration due to gravity (g) at that point is given by the formula:
g = GM/r^2
We can solve the second equation for M:
M = gr^2/G
Substitute M from the second equation into the first equation:
V = -g*r
Solve for r (distance from the center of the Earth to the point in space):
r = -V/g
Given that V = -5.12 x 10^7 J/kg and g = 6.4 m/s^2, we can find r:
r = -(-5.12 x 10^7 J/kg) / (6.4 m/s^2) = 8 x 10^6 m = 8000 km
The height h above the Earth's surface is the difference between r and the radius of the Earth (R):
h = r - R = 8000 km - 6400 km = 1600 km
So, the height of the point above the Earth's surface is 1600 km.
Similar Questions
An object of mass 12 kg is at a certain height above the ground. If the gravitational potential energy of the object is 480 J, find the height at which the object is with respect to the ground. (g = 10 ms–2)
Find the altitudes above the Earth's surface where Earth's gravitational field strength would be (a) five-sixths (enter first) and (b) one-sixth of its value at the surface.
Compute the value of g at a height of 4RE above the surface of the earth, given that the mass and radius of the earth (RE) have their usual values.*1 point0.39 m/s^20.42 m/s^20.49 m/s^23.90 m/s^2
The potential energy, in Joules, of an object is described by the formulaP.E. = mgh, where m = mass in kg, g = acceleration due to gravity in m/s2, andh = altitude in meters. Find the height above sea level of a 60 kg object with apotential energy equal to 4 × 106 Joules. Assume g = 10 m/s2. Round answer to the nearest meter.
The height at which the acceleration due to gravity decreases by 36% of its value on the surface of the earth is: (Assume radius of the earth is R) :-A B C D 4 R
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.