find the acceleration of a particle placed on the surface of the earth at the equator due to Earth's rotation the diameter of earth is equal to 12800km and it takes 24 hours for the earth to complete one Revolution about it axis
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Let ww be angular velocity of planet and 'R' its radius.
v=wRv=wR at equator -----(1)
g=g0−w2Rgg=g0−w2Rg at equator g0g0 at poles
g02g02=g0−w2R=g0−w2R
w2R=g02w2R=g02
v2=g0R2v2=g0R2 (Substituting from (1))
But we know escape velocity
ve=2g0R−−−−√ve=2g0R
=4v2−−−√=4v2
∴ve=2v
v=wRv=wR at equator -----(1)
g=g0−w2Rgg=g0−w2Rg at equator g0g0 at poles
g02g02=g0−w2R=g0−w2R
w2R=g02w2R=g02
v2=g0R2v2=g0R2 (Substituting from (1))
But we know escape velocity
ve=2g0R−−−−√ve=2g0R
=4v2−−−√=4v2
∴ve=2v
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