GATE Civil 2023 Set 2 | GA | Question: 10

Question

Consider a spherical globe rotating about an axis passing through its poles. There are three points $P, Q,$ and $R$ situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let $P, Q$, and $R$ move with speeds $v_P, v_Q$, and $v_R$, respectively.

Which one of the following options is CORRECT?

• A. $v_P<v_R<v_Q$
• B. $v_P<v_Q<v_R $
• C. $v_P>v_R>v_Q $
• D. $v_P=v_R \neq v_Q$

Comments

v=wR

Radius of rotation max at equator and min at poles.

Answer 1

Speed = Distance / Time. Here distance is diameter (D) of the Earth. Assuming same time unit for for each case for comparison.

Vp = D/T

Vq = D/(2T)

In case of Vr D is tending towards 0, so in same time unit is can cover huge ditance.

Hence, answer is C.

Answer 2

Velocity = ŵ.r

here , ŵ = angular rotation = constant 

hence, more is the distance away from the axis of rotation, more will be the velocity 

therefore, V_P > V_R > V_Q

_{Option (C)}

Answer 3

In a simple way, since, Speed ∝ Distance,

maximum Distance → maximum Speed

then,

•  the point Q at the pole almost covers NO Distance, so MINIMUM Speed
•  and the point P at the equator covers MAXIMUM Distance, so MAXIMUM Speed
•  and the point R between P and Q covers Distance > P and < Q

So, $$v_P > v_R > v_Q$$