A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with x (distance of the particle from the centre) according to
Net force towards centre of earth = mg' = mgxR
Normal force N = mg'sinθ
Thus pressing Force N = mgxRR2x
N= Mg2 constant and independent of x.
Hence (B) Tangential force F=ma=mg'cosθ
Q=g'cosθ=gx√R24−x2rx
α = gx √R2−4x2