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The escape velocity for a planet is Ve. A tunnel is dug along a diameter of the planet and a small body is dropped in at the surface. When the body reaches the centre of the planet, its speed will be: A. Zero B. Ve/2 C. Ve/(under root 2) D. Ve

The escape velocity for a planet is Ve. A tunnel is dug along a diameter of the planet and a small body is dropped in at the surface. When the body reaches the centre of the planet, its speed will be:
A. Zero 
B. Ve/2
C. Ve/(under root 2)
D. Ve

Grade:12th pass

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
2 years ago
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Vikas TU
14149 Points
2 years ago
Dear student 
The gravitational potential of surface of earth Vs = -Gm /R 
ravitational potential at the centre of earth can be given as : Vc = -3Gm /2R 
By conservation of energy , kinetic energy will be equal to change in momentum. 
V2 = 2Gm /R ( 3/2 – 1 )  = Gm /R = gR = Ve 2 /R 
Ve = 2gR 
V = Ve /2 
Hope this helps , 
Cheers 
 

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