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 period $v_1$ and $v_2$ be the maximum speed of the particle 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)

The correct options are
A $T_1=T_2$
D $v_1>v_2$

Time period $T=2\pi \sqrt{\frac{R}{g}}$
Therefore, time period is independent of amplitude.
$V_{\text{max}}=A\omega$
Amplitude is different.
It is recommended to remember the above formula of time period.