Question

The place at which plane of vibration of Foucault's pendulum does not rotate at all, is:

• A. Pole
• B. Equator
• C. Tropic of Cancer
• D. Tropic of Capricorn

Hint:

Visualize the Earth's rotation. At the poles, an observer is simply spinning in place, so the pendulum's plane appears to rotate a full circle in 24 hours. At the equator, an observer is carried along without any local twisting motion, so the pendulum's plane remains fixed relative to the ground.

Answer 1

The Correct Option is B

Step 1: Recall the formula for the rate of precession of a Foucault pendulum.The angular speed \(\omega_P\) of the precession of the plane of oscillation is given by:\[ \omega_P = \Omega \sin\phi \]where \(\Omega\) is the angular speed of the Earth's rotation, and \(\phi\) is the latitude of the pendulum's location.
Step 2: Determine the condition for no rotation.For the plane of vibration to remain stationary (no rotation), the rate of precession \(\omega_P\) must be zero.\[ \Omega \sin\phi = 0 \]
Step 3: Solve for the latitude \(\phi\).Given that the Earth is rotating, \(\Omega eq 0\). Therefore, the equation simplifies to:\[ \sin\phi = 0 \]This condition is satisfied when the latitude \(\phi = 0^{\circ}\).
Step 4: Identify the geographical location corresponding to this latitude.A latitude of \(0^{\circ}\) corresponds to the Earth's Equator. At the North or South Pole, where \(\phi = \pm 90^{\circ}\), \(\sin\phi = \pm 1\), resulting in maximum precession.