Q. Two tunnels are dug from one side of the earth's surface to the other side, one along a diameter and the other along a chord. Now two particles are dropped from one end of each of the tunnels. Both the particles oscillate simple harmonically along the tunnels. Let and be the time periods and and be the maximum speed of the particles in the two tunnels. Then :

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A

B

C

D

Solution:

As the force along both the tunnels at a distance from tunnel center are same, the angular frequency of oscillations of both the particles will be same hence but the tunnel along the chord is shorter hence the maximum speed at center in this case will be less.

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