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Question

If all objects on the equator of the earth feel weightless then the duration of the day will nearly become

A
6.2 hr
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B
4.4 hr
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C
2.2 hr
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D
1.412 hr
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Solution

The correct option is B 1.412 hr
We know that acceleration due to gravity at equator is,
ge=gRω2
where, ω0 is the angular velocity of the earth.
Angular velocity of Earth=2πT=2π86400
If the acceleration due to gravity at the equator becomes zero, the body at equator experiences weightlessness.
Let ω be the angular velocity of rotation at which the acceleration due to gravity at the equator becomes zero.
That is,
ge=gRω2=0
g=Rω2
ω=gR
Now, ωω0=1ω0gR=864002π9.86.4×106=17
ω=17ω0
Thus, the earth should rotate 17 times faster than the present rate.
Rotation speed increases by a factor of 17.
the duration of day decreases by factor 17.
New duration of day, T=2417=1.412hr

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