Physics

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satis · Answer

mass of the earth is m and radius is rmass of the particle is msuppose at some instant the particle is at radial distance r from centre of earth o. since, the particle is costrained to move along the tunnel , we define its position as distance x from c, where c the middle of the tunnel.  the particle make an angle θ at centre of earth o with c at intant. hence, equation of motion of the particle is :fx = m*axthe  gravitational force on the particle is f = gmmr/r^3since the particle is moving towards the center of the earth o,fx =  - f sin θ=  - ( gmmr/r^3 ) (x/r)=   - gmmx/r^3since fx ∝ -x, the motion is shm. fx =  - gmmx/r^3max =  - gmmx/r^3ax =  - gmx/r^3time period t = 2𝝅√( x/ax) = 2𝝅√(r^3 /gm)thus, the time taken by the particle to go from one end to other through the tunnel ist = t?2 = 𝝅√(r^3 /gm)

Category:	Physics
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Due Date:	10 August 2023, 12:08
Added:	9 August 2023, 00:26

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Physics

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