Force F is given in terms of time t and distance x by F= A sinCt+ B cosDx. Then dimensions of (A)/(B) and (C)/(D) are

Force F is given in terms of time t and distance x by F= A sinCt+ B co

1.	Force F is given in terms of time t and distance x by F= A sinCt+ B cosDx. Then dimensions of (A)/(B) and (C)/(D) are
Answer» `[M^(0)L^(0)T^(0)], [M^(0)L^(0)T^(-1)]` `[MLT^(-2)],[M^(0)L^(-1)T^(0)]` `[M^(0)L^(0)T^(0)],[M^(0)LT^(-1)]` `[M^(0)LT^(-1)],[M^(0)L^(0)T^(0)]` Solution :As `[A]= [F]` and `[B]= [F]` `:. [(A)/(B)]= ([F])/([F])= [M^(0)L^(0)T^(0)]` As `sintheta` is dimensionless, `:. [Ct]= 1` or `[C]=(1)/([t])= (1)/([T])= [T^(-1)]` `[DX]=1` or `[D]= (1)/([X])= (1)/([L])= [L^(-1)]` `:. [(C)/(D)]= ([T^(-1)])/([L^(-1)])= [M^(0)LT^(-1)]`