Find wight of the body of mass 200 kg on the earth at equator and at the latitude of `30^(@)` [ Take R= 6400 km]

Options

A. 1953 and 1955 N
B. 1960 and 1965 N
C. 1860 and 1800 N
D. None of these

Explanation

Given mass m - 200 kg and radius R= 6400 km
angular velocity of the earth `omega=(2pi)/(T)`
`=(2pi)/(24xx60xx60)=(2pi)/(86400) rarr omega = 7.268xx10^(-5) rads^(-1)`
find the weight of the body at the equator `lambda=0`
`therefore` Acceleration due to gravity at equator g=g -`R omega^(2) cos lambda`
`=9.8-0.03379=9.766`
weight at equator = mg `=200xx9.766=1953` N
at latitude givn `lambda=30^(@)`
`cos 30^(@)=sqrt(3)/(2)=0.866`
Therefore at the latitude of `30^(@)` the weight of the body
`m(g-R omega^(2) cos 30^(@))`
`=200xx9.770734 N=1954.14 N`