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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 $ν_{1}$ and $ν_{2}$ be the maximum speed of the particles in the two tunnels. Then

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$T_{1} = T_{2}$

$T_{1} > T_{2}$

$ν_{1} = ν_{2}$

$ν_{1} > ν_{2}$

answer is A, D.

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Detailed Solution

Time period in both the cases comes out to be

$T_{1} = T_{2} = 2 π \sqrt{\frac{R^{3}}{G M}} = 84.6 m i n$

But $ν_{1} > ν_{2},$ Because the difference in potential energy between the extreme position and mean position will be more in the first case.

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