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
Suppose, the acceleration due to gravity at the earth's surface is 10 m s−2 and at the surface of Mars it is 4⋅0 m s−2. A 60 kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the following figure best represents the weight (net gravitational force) of the passenger as a function of time?
Find the height over the Earth's surface at which the weight of a body becomes half of its value at the surface.
What is the acceleration due to gravity on the top of Mount Everest? Mount Everest is the highest mountain peak of the world at the height of 8848 m. The value at sea level is 9.80 m s−2.
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.
A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 m s−1. What should be the radius of the sphere?
If the acceleration due to gravity becomes 4 times its original value, then escape speed ____________.
Explain the variation of g with altitude.
Suppose we go 200 km above and below the surface of the Earth, what are the g values at these two points? In which case, is the value of g small?
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?
A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s2. The height of the bridge and velocity with which the pebble strikes the water will respectively be ______.
