Answer:
Let g’ be the acceleration due to gravity of the earth inside the earth
g’ = g(1-d/R)
R-d = y
g’ = g y/R
F = -mg y/R
F is proportional to (-y)
The motion is SHM when the body is in a tunnel.
ma = -mg’
T = 2π √R/g
A tunnel is dug through the centre of the earth. Show that a body of mass ‘m’ when dropped from rest from one end of the tunnel will execute simple harmonic motion.
A tunnel is dug through the centre of the earth. Show that a body of mass ‘m’ when dropped from rest from one end of the tunnel will execute simple harmonic motion.