Question

Force on a particle in one-dimensional motion is given by F = Av + Bt + Cx/At + D
where F = force, v = speed, t = time, x = position and A, B, C and D are constants. Dimension of C will be-​

Answer 1

Answer:

[M^2 L^-2]  

Explanation: "quantities of same dimensions are added or subtracted or divided"

dim(C)=dim[F(At+D)/x]                                                                                           which is equal to dim[(F/x)(F/tv)]  ; since dim (A) will be equal to dim(F/v)                                                           so,DIM(C)=dim[(F^2*t)/xv]  ----------->eq '1'            ;    which is equal to                                                                                                                                                  dim[F^2/v^2]=[M^2T^-2] ; we have written t/x as 1/v so i have taken the final form as F^2/v^2                                                                                                                             you may calculate it from eq '1' directly if you would like to do so                                   Hope you may understand it.