Question

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole [EAMCET (Med.) 1995]
A) Doubles B) Becomes half C) Remains same D) Becomes zero

Answer 1

Gravity at poles Should remain same

Answer 2

Answer:

At the north pole, the acceleration due to gravity (g) remains constant, i.e. (C).

Explanation:

The gravitational acceleration at the poles is calculated as follows:

$g'=g-\omega^2Rcos\theta$     (1)

Where,

g'=gravitational acceleration at the poles

g=gravitational acceleration on the earth's surface

ω=angular speed of the earth

R=radius of the earth

θ=angle of rotation of the earth

At the poles "θ=90°".

We get the following when we put the value of θ=90° in equation (1):

$g'=g-\omega^2Rcos 90\textdegree$

$g'=g$        (2)                  (cos90°=0)

As a result of equation (2), we can conclude that the value of gravity's acceleration does not vary, i.e. it remains constant (C).

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