Question

The rotation of the earth having radius R about its axis speeds upto a value such that a man at latitude angle 60^ feels weightless. The duration of the day in such case will be:

• A. 8π√((R)/(g))
• B. 8π√((R)/(3g))
• C. π√((R)/(g))
• D. 4π√((g)/(R))

Hint:

For rotation of earth problems, use effective gravity concept carefully.

Answer 1

The Correct Option is B

Step 1: For weightlessness, effective gravity must be zero: gλ = ω² Rλ
Step 2: At latitude λ = 60^, ω² R = (g)/(3)
Step 3: Angular speed, ω = √((g)/(3R))
Step 4: Time period, T = (2π)/(ω) = 2π√((3R)/(g)) = 8π√((R)/(3g))