Question

When a body is taken from poles to equator on the earth, its weight

• A. Increases
• B. Decreases
• C. Remains the same
• D. Increases at south pole and decreases at north pole

Answer 1

Answer: (B)

Decreases

$g^{\prime }=g-R{\omega }^{2}cos\left(2\lambda \right)$

g′=g−Rω2cos2⁡where ωω is the angular velocity of rotation of earth about its polar axis, RR is the radius of the earth and λλ is the latitude of a plac
At poles, $\lambda =90$

λ=90

$\therefore g_{p}ole=g-R{\omega }^{2}cos(2\times 90)$
∴gpole=g−Rω2cos2⁡90o=g
at equator $\lambda =0$
gequator=g−Rω2cos20o=g−Rω2<ggequator=g−Rω2cos2⁡0o=g−Rω2<g

$g_{e}quator=g-R\left(\omega {)}^{2}cos\right(2\times 0)=g-R(\omega {)}^2$
Thus, the acceleration due to gravity decreases from poles to equator
Hence, when a body is taken from poles to equator on the earth, its weight decreases