Here U0 denote energy , X0 is postion then what would be the dimension of "Q" ?
Answers
Answer:
Q = [ MLT^(-2) ]
Explanation:
If you look at the quantity Q and relation for it:
* apology for not using original symbols as it is not in my typeboard.
Q = {u0/Bx0} × log(Bm/at)
Here, logarithm is always a ratio of two quantities having the same dimensions. So, a logarithmic function has no dimension. So you can very well logically and with reason ignore the log part.
What remains?
Q = u0/Bx0
This only determines the dimension of Q
#
u0 represents energy here, so it will have the dimension of energy.
Energy = mass × (velocity of light)^2.
= [ M ] × [ LT^(-1) ]^2
= [ ML^2T^(-2) ].
* famous E = mc^2.
#
B is a constant and hence have no dimension, just a number. You can forget B also.
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x0 is position. And generally defined using length.
Dimension of position = [ L ]
so we finally have:
Q = {u0/Bx0} × log(Bm/at)
Q = [ ML^2T^(-2) ] / [ L ]
Q = [ MLT^(-2) ]
And Q is actually referring to physical quantity force. You just have to divide dimension of energy with dimension of length!! Isn't simple??