Advertisements
Advertisements
प्रश्न
Explain the variation of g with altitude.
उत्तर
Consider an object of mass m at a height h from the surface of the Earth. Acceleration experienced by the object due to Earth is
g’ = `("GM")/(("R"_"e" + "h")^2)`
Mass at a height h from the center of the Earth
g’ = `("GM")/("R"_"e"^2 (1 + "h"/"R"_"e")^2)`
g’ = `("GM")/("R"_"e"^2) (1 + "h"/"R"_"e")^-2`
If h << Re
We can use Binomial expansion. Taking the terms up to first order
g’ = `("GM")/("R"_"e"^2) (1 - 2"h"/"R"_"e")`
g’ = `"g" (1 - 2"h"/"R"_"e")`
We find that g’ < g. This means that as altitude h increases the acceleration due to gravity g decreases.
APPEARS IN
संबंधित प्रश्न
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?
If the acceleration due to gravity at the surface of the earth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is
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.
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 ____________.
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?
The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity ______.
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 ______.
