Tardigrade
Question
Physics
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 T1 and T2 be the time periods and v1 and v2 be the maximum speed of the particles in the two tunnels. Then :

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 $T_{1}$ and $T_{2}$ be the time periods and $v_{1}$ and $v_{2}$ be the maximum speed of the particles in the two tunnels. Then :

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$T_{1}=T_{2}$

$T_{1}>T_{2}$

$v_{1}=v_{2}$

$v_{1}>v_{2}$

Solution:

As the force along both the tunnels at a distance $x$ from tunnel center are same, the angular frequency of oscillations of both the particles will be same hence $T_{1}=T_{2}$ but the tunnel along the chord is shorter hence the maximum speed at center in this case will be less.

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