Question

Let force \( F = A \sin(Ct) + B \cos(Dx) \) where \( x \) and \( t \) are displacement and time respectively. The dimensions of \( \frac{C}{D} \) are same as dimensions of

• A. Angular velocity
• B. Angular momentum
• C. Velocity gradient
• D. Velocity

Hint:

When solving questions involving force equations with sine and cosine functions, relate the coefficients of time and displacement to their respective physical quantities, such as angular velocity.

Answer 1

The Correct Option is A

Step 1: Understanding the given force equation.
The given force equation \( F = A \sin(Ct) + B \cos(Dx) \) involves both time (\( t \)) and displacement (\( x \)). The terms \( C \) and \( D \) are related to the rates of change of force with respect to time and displacement, respectively.
Step 2: Relationship between \( \frac{C}{D} \) and angular velocity.
The term \( C \) has the dimensions of angular frequency (time inverse) and \( D \) has the dimensions of wavenumber (inverse of length). Therefore, the ratio \( \frac{C}{D} \) has dimensions of angular velocity.
Step 3: Conclusion.
Thus, the correct answer is (A) Angular velocity.