Find the distance from the Earth's surface at which the acceleration due to gravity has the same value whether you go that distance above the surface or below it. (R is the Earth's radius.)

x = R(sqrt(5) - 1)/2
x = R/2
x = R(sqrt(5) + 1)/2
x = R/3

Correct answer: x = R(sqrt(5) - 1)/2

Solution

Equate the gravity value at height x above the surface to the value at depth x below, then solve the resulting algebraic equation.

Related JEE Advanced Physics questions

Two objects, each with a mass of M, are positioned at a fixed distance of 2L apart. A smaller particle of mass m is launched from the midpoint of the line connecting their centers, moving in a direction perpendicular to this line. Given the gravitational constant G, which of the following statements is accurate?
A central force is given as F(r) = −k / rⁿ, where k is a constant. What condition must n satisfy for a circular orbit to remain stable?
Which of the following correctly represents the relationship |F| = dU/dr?
Two objects, each with mass M, are placed at a fixed distance of 2L apart. A particle of mass m is launched from the midpoint between these two objects in a direction perpendicular to the line connecting them. Given the gravitational constant G, which of the following statements is accurate?
Consider a spherical gaseous cloud of mass density ρ(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particle is their mutual gravitational force. If ρ(r) is constant in time, the particle number density n(r) = ρ(r)/m is (G is universal gravitational constant).
A particle with mass m is influenced by the gravitational force of a much larger mass M (M >> m). The particle orbits in a circular path of radius r₀ with a time period T₀. An additional central force is introduced, arising from the potential energy V(r) = αmα/r³, where α is a positive constant with appropriate units and r is the orbital radius. If the particle continues to move in the same circular orbit of radius r₀ under the combined gravitational and additional potential, but its time period changes to T₁, what is the value of (T₁² - T₀²)/T₀²? [G represents the gravitational constant.]

⚔️ Practice JEE Advanced Physics free + battle 1v1 →