Find the dimensions of `(axxb)/(c )` in the relation `F =(a)/(sqrtx) +bx = cx^2` where F is force and x is distance.

Answer

`ML^(5//2)T^(-2)`

Explanation

The given relation is `F = (a)/(sqrtx) + bx +cx^2`
As `(a)/sqrtx = F, a= sqrtx F =L^(1//2)(MLT^(-2)`
` = [ML^(3//2)T^(-2)]`
Again,`bx = F, b = (F)/(x) = (MLT^(-2))/(L) = [M L^1 T^(_2)]`
Also, `cx^2 = F,c= (F)/(x^2) = (MLT^(-2))/(L^2) = [M L^(-1) T^(-2)]`
Now, `(axxb)/(c ) = ((ML^(3//2)T^(-2))xx(M^(1)T^(-2)))/((ML^(-1)T^(-2)))`
`=[ML^(5//2) T^(-2)]`