What should be the angular velocity of the Earth, so that bodies lying on equator may appear weightless? How many times this angular velocity is faster than the present angular velocity?(Given; g = 9.8 m/s²; R = 6400 km)
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w₀ = present angular velocity = 2π / 86400 rad/sec
w = new angular velocity
centripetal force on the objects at equator = m R w²
gravitational pull = G M m / R² = m g
Apparent weight = m g' = m g - m R w²
g' = 0 when w² = g/R
w = √(g/R)
Substitute the values to get answer.
Ratio = w/w₀ = 86400 √(g/R) / 2π
w = new angular velocity
centripetal force on the objects at equator = m R w²
gravitational pull = G M m / R² = m g
Apparent weight = m g' = m g - m R w²
g' = 0 when w² = g/R
w = √(g/R)
Substitute the values to get answer.
Ratio = w/w₀ = 86400 √(g/R) / 2π
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