Question

The weights of two objects one lying at the equator and the other at latitude `45^(@)` on earth and 100 N each. If the angular velocity of rotation of earth increases such that the object at the equator becomes weightless (zero N), the weight of the object at latitude `45^(@)` will be
A. 100 N
B. 50 N
C. 25 N
D. 0 N

Answer 1

Correct Answer - b
`g_(phi)=g-Romega^(2)cos^(2)phi`
`g_(phi)=g-(Romega_(1)^(2))/(2)`
For weightlessness condition at the equation `omega_(1)=sqrt((g)/(R))`
`g_(phi)=g-(R)/(2)=(g)/(2)`
`W=mg_(phi)=(mg)/(2)=(100)/(2)=50N.`