Numericals:- 01 Write the dimensions of a/b in the relation :- F=ax+bt² where F is force, x is distance and t is time
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Numericals:- 01 Write the dimensions of a/b in the relation :- F=ax+bt² where F is force, x is distance and t is time
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What are the dimensions of 'a' and 'b' in the relation: F= a+bx, where F is force and x is distance?
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SAMBIT CHAKRABORTY Badi
, INISTITUTE OF ENGINEERING AND MANAGEMENT , CSE BRANCH
Answered October 4, 2016
By dimensional analysis we consider both the LHS and RHS have the same dimensions.
F=a+bx
In the given equation the LHS is F which stands for force
[F] = [MLT^-2 ]
now in RHS we have two constants a & b , by additive property we find that a and F will have the same dimension .
Thus [a] = [ MLT^ -2]
Now for…. bx , we know x is distance so it has dimension x= [ L ]
Thus we get bx = [ MLT ^-2]
=> b[ L ]= [ MLT ^-2]
=>. b= [ MT ^-2]
a= [MLT ^-2 ] & b=[MT ^-2 ]
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