A particle of mass \( m \) is dropped from a great height \( h \) above the hole in the earth du...

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A particle of mass \( m \) is dropped from a great height \( h \) above the hole in the earth dug along its diameter.
(a) The motion of the particle is simple harmonic
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(b) The motion of the particle is periodic
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(c) The speed of the particle at the centre of earth equals \( \sqrt{\frac{2 G M}{(R+h)}} \), where \( R \) and \( M \) are the radius and mass of the earth respectively
(d) The speed of the particle at the centre of earth equals \( \sqrt{\frac{G M(R+3 h)}{R(R+h)}} \), where \( R \) and \( M \) are the radius and mass of the earth respectively
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