InterviewSolution
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InterviewSolution
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If the centripetal force is of the form `m^a v^b r^c`, find the valus of a,b, and c. |
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Answer» According to the provided information , `F prop m^(a) v^(b) r^( c ) ` rArr `F = km^(a) v^(b) r^(c ) ` ….(i) Where `k` is the dimensionless constant of proportionality and `a , b, c` are the constant powers powers of `m , v , r`, respectively. Now using the principle of homogenity , comparing the power of like quantities on both the sides , we have ` a = 1 ( ii) b + c = 1 (iii) and b = 2 (iv) Using (ii) , (iii) , and (iv) , we have a = 1 , b = 2 , and `c = -1`. Using (ii) , (iii) , and (iv), we have ` a = 1 , b = 2 , c = -1`. Using these values in (i) , ` F = km^(1) v^(2) r ^(-2)` `implies F = K (mv^(2))/(r)` which is the desired relation. |
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