In the following equation, x, t and F represent respectively, displacement, time and force:F = a + bt + (1)/(c+d. x)+ Asin(omegat+phi) The dimensional formula for A. d is

In the following equation, x, t and F represent respectively, displace

1.	In the following equation, x, t and F represent respectively, displacement, time and force:F = a + bt + (1)/(c+d. x)+ Asin(omegat+phi) The dimensional formula for A. d is
Answer» `[T^(-1)]` `[L^(-1)]` `[M^(-1)]` `[TL^(-1)]` Solution :`F= a+ BT+ (1)/(c+d.x)+ Asin(omegat+phi)` As `sin(omegat+phi)`is dimensionless, therefore A has dimensions of FORCE. `:. [A]= [F]= [MLT^(-2)]` As each term on RHS represents force `:. (1)/(c+d. x)= F` or `(1)/(c)= F` `:. [c]= (1)/([F])= (1)/([MLT^(-2)]= [M^(-1)L^(-1)T^(2)]` As c is added to d.x therefore dimension of c are same that of d.x `:. [d.x]= [c]` or `[d]= ([c])/([x])= ([M^(-1)L^(-1)T^(2)])/([L])= [M^(-1)L^(-2)T^(2)]` The dimensional FORMULA for `A.d = [MLT^(-2)][M^(-1)L^(-2)T^(2)]= [L^(-1)]`