The escape velocity from a planet is Ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be(a) Ve (b) Ve/√2(c) ve/2 (d) zero
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the speed will be root2 c
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Answer:
D) Zero
Explanation:
Escape velocity = Ve
Gravitational potential at the surface of the earth = Vs = -GM/R
Gravitational potential at the center of earth = Vc = -3GM/2R
By the conservation of energy = 1/2mv² = m (Vs-Vc)
= v²= 2GM/r[3/2-1]
Since centre of earth R = 0 and gravitational acceleration is also zero, thus the speed of body when it reaches the ground will also be zero.
Speed = v = (2gR)-1/2 = 0
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