Question

find the dimensional formula for a and b in a/t^2=FV+b/x^2 where F is force and V is velocity​

Answer 1

answer : dimension of a = [ML^2T^-1]

dimension of b = [ML^4T^-3]

explanation : formula is ... $\frac{a}{t^2}=FV+\frac{b}{x^2}$

where F is force and V is velocity.

we know, dimension of F = [MLT^-2]

dimension of V = [LT^-1]

dimension of (a/t²) = dimension of (FV)

dimension of a = dimension of t² × dimension of F × dimension of V

= [T²] × [MLT^-2] × [LT^-1]

= [ML^2T^-1]

again, dimension of (FV) = dimension of (b/x²)

or, dimension of F × dimension of V × dimension of x² = dimension of b

or, [MLT^-2] × [LT^-1] × [L^2] = dimension of b

or, dimension of b = [ML^4T^-3]