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Spring Block's Time Period

Imagine a nar...

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Imagine a narrow tunnel between the two diametrically opposite points of the earth. A particle of mass m is released in this tunnel. The time period of oscillation i

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Q. If a straight tunnel is bored connecting two points on the surface of the earth, then the time taken by a particle released from any point of the tunnel, to come to instantaneously rest again in the tunnel is

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 smooth and bottomless tunnel is dug through the centre of earth. A particle is released from the surface of earth into the tunnel. Time to reach centre of tunnel is (approximately) equal to (where

R =

Radius of earth).

Q. Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance

(\frac{R}{2})

from the earth's centre, where

R

is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

Q. A tunnel is dug along the diameter of the earth. Two balls of mass

m

2 m

are dropped from the opposite ends of the tunnel simultaneously. They collide in the tunnel and stick to each other. If the new amplitude of their oscillation is

\frac{R}{n}

R

is earth's radius, then the value of

n

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