Question:
A cosmonaut is orbiting earth in a spacecraft at an altitude h = 630 km with a speed of 8 k$ms^{ - 1}$. If the radius of the earth is 6400 km, the acceleration of the cosmonaut is
A cosmonaut is orbiting earth in a spacecraft at an altitude h = 630 km with a speed of 8 k$ms^{ - 1}$. If the radius of the earth is 6400 km, the acceleration of the cosmonaut is
Updated On: Jul 5, 2022
- $ 9.10 ms^{ - 2} $
- $ 9.80 ms^{ - 2} $
- $ 10.0 ms^{ - 2} $
- $ 9.88 ms^{ - 2} $
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The Correct Option is A
Solution and Explanation
Given, $ v = 8 \, kms^{ - 1} = 8000 \, ms^{ - 1} $,
r = (6400 + 630) km = (6400 + 630) $ \times $ 1000 m
a = $ \frac{ v^2 }{ r} $
a = $ \frac{ ( 8000)^2 }{ ( 6400 + 630 ) \times 1000 } $
= $ 9.10 \, ms^{ - 2 } $
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration