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Motion Under Gravity

if ge is the ...

Question

if ge is the acceleration due to gravity at the equator and gp be the that at the poles. assuming the earth to be a a sphere of radius Re roatating about its own axis with angular speed omega, then ge-gp is ?

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Q. The acceleration due to gravity at the poles and the equator is

g_{p}

g_{e}

respectively. If the earth is a sphere of radius

R_{E}

and rotating about its axis with angular speed

ω

g_{p} - g_{e}

is then given by

R

is the radius of earth,

ω

is its angular velocity and

g_{p}

is the value of acceleration due to gravity at the poles, then effective value of acceleration due to gravity at the latitude

λ = 60^{o}

will be equal to

Q. If earth were to rotate on its own axis such that the weight of a person at the equator becomes half the weight at the poles, then its time period of rotation is: (

g

=acceleration due to gravity near the poles and

R

is the radius of earth) (Ignore equatorial bulge)

Q. In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be

(g = 10 m s^{- 2} a n d r a d i u s o f e a r t h i s 6400 k m)

Q. Earth radius is

R

and spin angular velocity of Earth is

ω

. At what height above the North pole the acceleration due to gravity will be same as that at the equation? (

g

is acceleration due to gravity at North pole).

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