A tunnel is dug along the chord of the earth at a perpendicular distance 2 R from the earth's centre. Walls of tunnel are frictionless. A particle of mass m is released into tunnel. Find the ra

Question

A tunnel is dug along the chord of the earth at a perpendicular distance $\frac{R}{2}$ from the earth's centre. Walls of tunnel are frictionless. A particle of mass m is released into tunnel. Find the ratio of normal reactions at point P & Q between tunnel and particle as shown in the figure.

Answer:

1

Solution:

Field at any position $R$ inside sphere $\propto R$

$∴ N \propto R cos θ \propto \frac{R}{2} ∴ N_{P} = N_{Q}$

TestHub · Accepted Answer

Field at any position R inside sphere ∝ R ​ ∴ N ∝ R cos θ ∝ 2 R ​ ∴ N P ​ = N Q ​ ​

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