A particle is released from a height S above the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of the Earth and the speed of the particle at that instant are respectively:
Options

Question

A particle is released from a height S above the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of the Earth and the speed of the particle at that instant are respectively:

Options

G1 Physics · Accepted Answer

Take the gravitational potential energy to be zero at the Earth's surface. Initially the particle is released from rest at height S, so its total mechanical energy is E = mgS. At the required point, K = 3U. Therefore, K + U = 4U = mgS. If the height at that instant is h, U = mgh. Hence, 4mgh = mgS ⇒ h = S/4. Now, K = 3U = 3mgS/4. Also, K = ½mv². Thus, ½mv² = 3mgS/4 ⇒ v² = 3gS/2 ⇒ v = √(3gS/2). Therefore the correct pair is S/4, √(3gS/2). Correct option: C.