Question

The acceleration of a frame of reference, fixed on the earth’s surface at the equator and rotating with the earth, once a day will be:

• A. \(3.4 \times 10^{-2} \, m/s^2\)
• B. \(0.004 \, m/s^2\)
• C. \(7.15 \times 10^7 \, m/s^2\)
• D. \(61.2 \, m/s^2\)

Hint:

For Earth’s rotation: - Use \( a = \omega^2 R \). - Earth’s rotation causes a small centripetal acceleration at the equator. - The effect is negligible in daily life.

Answer 1

The Correct Option is A

The centripetal acceleration at the equator due to Earth's rotation is:
\[ a = \omega^2 R \] where
\( \omega = \frac{2\pi}{T} \) is the angular velocity of the Earth (\( T = 86400 \) sec), \( R = 6.37 \times 10^6 \) m is the radius of the Earth. Substituting the values:
\[ a = \left(\frac{2\pi}{86400} \right)^2 \times (6.37 \times 10^6) \] \[ a \approx 3.4 \times 10^{-2} \text{ m/sec}^2 \] Thus, the correct answer is: