Using dimensional analysis, we can determine the dimensions of Q by analyzing the dimensions of the variables involved in the formula.
Let's start with the numerator:
- The square of the orbital radius has dimensions of length squared (L^2).
Now let's move on to the denominator:
- The radius of the earth has dimensions of length (L).
- The acceleration due to gravity has dimensions of length per time squared (LT^-2).
Putting it all together, we have:
Q = (L^2) / (L * LT^-2)^1/2
Simplifying the denominator:
Q = (L^2) / (L^2T^-2)^1/2
Q = (L^2) / (L)T^-1
Q = LT
Therefore, Q represents a quantity with dimensions of length times time, which is the unit for speed.
Therefore, the correct answer is: Orbital speed.
A student trying to calculate the parameters of a satellite orbit obtained a quantity Q which is related with the orbital radius
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�
,
radius of the earth
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�
and acceleration due to gravity,
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by the formula
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=
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�
�
2
�
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½
. Using dimensional analysis, find out what Q represents.
Select one:
Tangential force
Torque on the satellite
Centripetal acceleration
Orbital speed
1 answer
1 answer