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A ball of mass m is dropped from a heigh...

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`)

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 sped `upsilon = sqrt((2GM)/(R ))`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`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 ))`
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