Question

Force \( F = P \cos(Ax) + Q \sin(Bt) \), where \( x \) and \( t \) are displacement and time respectively. Which one of the following physical quantity has the dimensions of \( \frac{[B]}{[A]} \)?

• A. velocity gradient
• B. velocity
• C. angular velocity
• D. angular momentum

Hint:

In problems involving dimensions, always analyze the units and their relationship. The ratio of dimensions of time and length gives you velocity.

Answer 1

The Correct Option is B

Step 1: Analyzing the equation.
The dimensions of \( F \) are: \[ [F] = [P] \cdot [x] + [Q] \cdot [t] \] Assuming \( P \) and \( Q \) have the dimensions of force, and \( x \) has the dimension of length, and \( t \) has the dimension of time. Now, considering the dimensions of \( \frac{[B]}{[A]} \), this corresponds to velocity. Therefore, the correct answer is (B) velocity.