Question

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 :

• A. $T_{1}=T_{2}$
• B. $T_{1}>T_{2}$
• C. $v_{1}=v_{2}$
• D. $v_{1}>v_{2}$

Answer 1

Answer: (A), (D)

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.