Question

A ball of mass m is dropped from a height h equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Choose the correct options.

• A. Particle will oscillate through the earth to a height h on both sides
• B. Particle will execute simple harmonic motion
• C. Motion of the particle is periodic
• D. Particle passes the centre of earth with a speed $v=\sqrt{\frac{2GM}{R}}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Particle will oscillate through the earth to a height h on both sides
C Motion of the particle is periodic
D Particle passes the centre of earth with a speed $v=\sqrt{\frac{2GM}{R}}$

$K_i+U_i=K_f+U_f$
$\therefore$ $0-\frac{GMm}{2R}$
$=\frac{1}{2}m{v}^2-\frac{3}{2}\frac{GMm}{R}$
or $v=\sqrt{\frac{2Gm}{R}}$