Advertisements
Advertisements
Question
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?
Advertisements
Solution
d = 200 km = 200 × 103 m
RE = 6371 × 103 m
h = 200 km = 200 × 103 m
Variation of g’ with depth
g’ = `"g" (1 - "d"/"R"_"E")`
= `"g" (1 - (200 xx 10^3)/(6371 xx 10^3))`
= g (1 − 0.0314)
= g (0.9686)
g’ = 0.96 g
Variation of g’ with altitude
g’ = `"g" (1 - (2"h")/"R"_"E")`
= `"g" (1 - (2 xx 200 xx 10^3)/(6371 xx 10^3))`
= g (1 − 2(0.0314))
= g (0.9372)
g’ = 0.94 g
APPEARS IN
RELATED QUESTIONS
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?
The earth revolves round the sun because the sun attracts the earth. The sun also attracts the moon and this force is about twice as large as the attraction of the earth on the moon. Why does the moon not revolve round the sun? Or does it?
The acceleration of the moon just before it strikes the earth in the previous question is
A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Account for the earth's rotation only.
If the acceleration due to gravity becomes 4 times its original value, then escape speed ____________.
Explain the variation of g with altitude.
Explain the variation of g with depth from the Earth’s surface.
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)
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 ______.
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 ______.
