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Standard XII

Physics

Displacement of COM:Application

A tunnel is d...

Question

A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.

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Solution

Mass of earth, $M = (\frac{4}{3}) π R^{3} ρ \frac{M^{'}}{M} = \frac{x^{3}}{R^{3}}$

$∴$ Gravitational force on F
$= \frac{G M m}{x^{2}} \Rightarrow F = \frac{G M x^{3} m}{R^{3} x^{2}} = \frac{G M m}{R^{3}} x$

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A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.

Mass of earth, M=(43)πR3ρM′M=x3R3 ∴ Gravitational force on F =GMmx2⇒F=GMx3mR3x2=GMmR3x

Mass of earth, $M = (\frac{4}{3}) π R^{3} ρ \frac{M^{'}}{M} = \frac{x^{3}}{R^{3}}$

$∴$ Gravitational force on F
$= \frac{G M m}{x^{2}} \Rightarrow F = \frac{G M x^{3} m}{R^{3} x^{2}} = \frac{G M m}{R^{3}} x$