By Team Aakash Byju's | 23rd December 2022
In relation, F = a + bx, where F is the force and x is the distance. Calculate the dimensions of a and b.
The answer is dimensions of a = [MLT ] and dimensions of b = [MT ].
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According to the Principle of Homogeneity of Dimensions, in a dimensionally correct equation, the dimensions of the terms on both sides are the same.
Given that, F = a + bx and F is the Force. Further, two quantities can be added to give the third only if they all have the same units.
=> [F] = [a] = [bx]
Since F stands for Force, we know that the dimensions of F are [MLT ].
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Since [a] = [F] => [a] = [MLT ] and
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[bx] = [F] => [b] = [MLT ] ÷ [x]
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=> [b] = [MLT ] ÷ [L]
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∴ [b] = [MT ]
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(∵ x is the length)