Advertisements
Advertisements
प्रश्न
Explain the variation of g with latitude.
Advertisements
उत्तर
When an object is on the surface of the Earth, it experiences a centrifugal force that depends on the latitude of the object on Earth. If the Earth were not spinning, the force on the object would have been mg. However, the object experiences an additional centrifugal force due to the spinning of the Earth.
This centrifugal force is given by mω2R’.
OPz, cos λ = `"PZ"/"OP" = "R’"/"R"`
R’ = R cos λ
Variation of g with latitude
where λ is the latitude. The component of centrifugal acceleration experienced by the object in the direction opposite to g is
aPQ = ω2R’ cos λ = ω2R cos2 λ
Since R’ = R cos λ
Therefore, g’ = g – ω2 R cos2 λ
From the above expression, we can infer that at the equator, λ = 0, g’ = g – ω2R. The acceleration due to gravity is minimum. At poles λ = 90; g’ = g, it is maximum. At the equator, g’ is minimum.
APPEARS IN
संबंधित प्रश्न
If heavier bodies are attracted more strongly by the earth, why don't they fall faster than the lighter bodies?
An apple falls from a tree. An insect in the apple finds that the earth is falling towards it with an acceleration g. Who exerts the force needed to accelerate the earth with this acceleration g?
The acceleration of moon with respect to earth is 0⋅0027 m s−2 and the acceleration of an apple falling on earth' surface is about 10 m s−2. Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon towards the earth will be
Find the acceleration due to gravity in a mine of depth 640 m if the value at the surface is 9.800 m s−2. The radius of the earth is 6400 km.
A particle is fired vertically upward from earth's surface and it goes up to a maximum height of 6400 km. Find the initial speed of particle.
Explain the variation of g with altitude.
Calculate the change in g value in your district of Tamil nadu. (Hint: Get the latitude of your district of Tamil nadu from Google). What is the difference in g values at Chennai and Kanyakumari?
If R is the radius of the earth and g is the acceleration due to gravity on the earth's surface, the mean density of the earth is ______.
A ball is immersed in water kept in container and released. At the same time container is accelerated in horizontal direction with acceleration, `sqrt44` m/s2. Acceleration of ball w.r.t. container is ______ m/s2 (specific gravity of ball = 12/17, g = 10 m/s2)
If the radius of the earth shrinks by 2% while its mass remains the same. The acceleration due to gravity on the earth's surface will approximately ______.
