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Question: The radius of the earth is 6400 km and \(g = 10 \mathrm {~m} / \mathrm { sec } ^ { 2 }\) . In order ...

The radius of the earth is 6400 km and g=10 m/sec2g = 10 \mathrm {~m} / \mathrm { sec } ^ { 2 } . In order that a body of 5 kg weighs zero at the equator, the angular speed of the earth is

A

1/80 radian/sec

B

1/400 radian/sec

C

1/800 radian/sec

D

1/1600 radian/sec

Answer

1/800 radian/sec

Explanation

Solution

For the condition of weightlessness at equator

ω=gR\omega = \sqrt { \frac { g } { R } } ∴ ω=1640×103=1800rad/s\omega = \sqrt { \frac { 1 } { 640 \times 10 ^ { 3 } } } = \frac { 1 } { 800 } \mathrm { rad } / \mathrm { s }