- #1
tanaygupta2000
- 208
- 14
- Homework Statement
- A tunnel is dug from the surface of the earth through the center and opens at the other end. A ball is dropped from one end of the tunnel. The acceleration due to gravity on the earth’s surface is g and the radius of the earth is R. Assuming that the earth has a constant density, what is the time taken by the ball to reach the center of the earth?
Options:
(a) π√(R/g)
(b) 2π√(R/g)
(c) (π/2)√(R/g)
(d) (π/4)√(R/g)
- Relevant Equations
- Acceleration due to gravity inside the earth, g' = g(1 - d/R)
The value of acceleration due to gravity at a depth 'd' inside the Earth is given by-
g' = g(1 - d/R)
which can also be written as
g' = g(x/R) from the diagram
so that x'' = (w2)x
where w2 = g/R is the angular frequency
Hence the time period T is given by
T = 2π sqrt(R/g)
but the question is asking only for the half journey
so the answer should be
T = π sqrt(R/g)
Is this correct?