2) A tunnel is dug along a diameter of the earth If M and R are the mass and - Physics - Gravitation

Question

2) A tunnel is dug along a diameter of the earth If M and R are
the mass and radius respectively of earth, then the force on a
particle of mass 'm' placed in the tunnel at a distance r from the
center is
A) GMmr/R^3 B) GMm/rR^3 C) GMmR^3/r D) GMmr/R^2

Neha Gupta · Accepted Answer

Gravitational force of attraction is given by:

F = GM1M2r2
M1 be the mass of the earth from centre to distance
r
M2 be the mass of the particle placed at a distance r
from the centre

M1 = ρ × volume ρ is the density of the earthM1 =
M(4/3)πR3(4/3)πr3where M is the mass of the earth and Ris
the radius of the earth M1 = Mr3R3

Force is given by:

F = GMr3R3mr2 = GMmrR3

Hence option (A) is correct

2) A tunnel is dug along a diameter of the earth. If M and R are the mass and radius respectively of earth, then the force on a particle of mass 'm' placed in the tunnel at a distance r from the center isA) GMmr/R^3 B) GMm/rR^3 C) GMmR^3/r D) GMmr/R^2

2) A tunnel is dug along a diameter of the earth. If M and R are the mass and radius respectively of earth, then the force on a particle of mass 'm' placed in the tunnel at a distance r from the center is
A) GMmr/R^3 B) GMm/rR^3 C) GMmR^3/r D) GMmr/R^2