Time period of oscillations of a particle along a tunnel inside the earth at a distance x from the centre

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Q. A particle of mass

50 kg

thrown into the tunnel from point

A

inside the earth, the tunnel is

d

away from the center of the earth. A particle oscillates about a point

C

inside the tunnel due to the gravitational force towards the centre. Calculate the time period of oscillation. (Radius of earth

= 6.378 \times 10^{6} m)

Q. 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.

Q. A tunnel is dug along a diameter of earth. The force on a particle of mass

m

and distance

x

from the centre in this tunnel will be :

Q. 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. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R/2 from the earth's centre where R is the radius of the earth. The wall of the tunnel is frictionless.

(a) Find the gravitational force exerted by the earth on a particle of mass m placed in the tunnel at a distance x from the centre of the tunnel.

(b) Find the component of this force along the tunnel and perpendicular to the tunnel.

(e) Show that the motion of the particle in the tunnel is simple harmonic and find the time period.

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