Question

Let force F = A sin(Ct) + B cos(Dx), where x and t are displacement and time, respectively. The dimensions of `"C"/"D"` are same as dimensions of

Options

• angular velocity

• velocity

• angular momentum

• velocity gradient

Answer 1

velocity

Explanation:

Given, force, F = A sin(Ct)+ Bcos(Dx) Here, (Ct) and (Dx) are dimensionless as they represents angles.

`therefore ["C"]=1/["t"]=["T"^-1]`

and `["D"]=1/["x"]=["L"^-1]`

Dimensions of `[["C"]]/[["D"]]=[["T"^-1]]/[["L"^-1]]=["LT"^-1]`

This is same as the dimensions of velocity.