IIT JEE , AIEEE Forum - Physics , Mechanics

edison

Q) if the earth were to complete a day in 1 hr then wat wud be the weight of man as registrd on a weighing machine?

Sol) Effect of rotation of earth on weight mg of an object is given by

Efective weight = W' = m(g-w²rcos²A)

where W = mg = weight in the absence of rotation

w = angular speed of the earth

A = Latitude of earth at the point where object is kept

A = 0 deg, at equator (thus effect od rotationis maximum on equator)

= 90 deg, at poles, (thus effect is nil at the poles)

Now if earth completes its rotation in 1hr, then itsangular speed is increased by 24 times,

thus w' = 24w

So the weight mg of the man will be

W'' = m(g- 576w²rcos²A)

Thus W'' = m(g-w²rcos²A) - 575mw²rcos²A

or W'' = W' - 575mw²rcos²A

Thus teh weight of man is reduced by a 575w²rcos²A on weighing machine