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 shows in the figure. Choose the correct options. (Mass of earth `= M`)

Options

A. (a)Particle will oscillate through the earth to a height `h` on both sides
B. (b)Particle will execute simple harmonic motion
C. (c)Motion of the particle is periodic
D. (b)Particle passes the centre of earth with a sped `upsilon = sqrt((2GM)/(R ))`

Answer

A, C, D

Explanation

`K_(i) + U_(i) = K_(f) + U_(f)`
`:. 0 - (GMm)/(2R ) = (1)/(2) m nu^(2) - (3)/(2) (GMm)/(R)`
or `nu = sqrt((2GM)/(R ))`