Question

If a body is performing uniform circular motion with velocity \( v \) and radius \( R \), then identify the true statements from the following:
A. Its velocity \( v \) is constant.
B. Acceleration is always directed towards the centre and its magnitude is \( a = \frac{v^2}{R} \).
C. Angular momentum is constant in magnitude but its direction keeps changing.
D. Angular velocity of the body \( = \frac{v}{R} \). 
Choose the most appropriate answer from the options given below.

• A. A and C only
• B. B and D only
• C. A, B, and D only
• D. A and D only

Hint:

In uniform circular motion, the speed is constant, but the velocity changes direction continuously. Centripetal acceleration keeps the object in circular motion, always pointing towards the center of the circle.

Answer 1

The Correct Option is C

Step 1: Understand the nature of uniform circular motion.
In uniform circular motion:
The speed \( v \) of the body remains constant.
The velocity is constantly changing direction because the body is moving along a circular path.
The acceleration is directed towards the center of the circle (centripetal acceleration), and its magnitude is given by \( a = \frac{v^2}{R} \).
Step 2: Analyze each statement.
A. Its velocity \( v \) is constant: This is true. In uniform circular motion, the speed (magnitude of velocity) is constant, but the direction of the velocity changes continuously.
B. Acceleration is always directed towards the centre and its magnitude is \( a = \frac{v^2}{R} \): This is true. In uniform circular motion, the acceleration (centripetal acceleration) always points towards the center of the circle, and its magnitude is \( a = \frac{v^2}{R} \), where \( v \) is the velocity and \( R \) is the radius of the circle.
C. Angular momentum is constant in magnitude but its direction keeps changing: This is true. The magnitude of angular momentum \( L \) is constant because the speed and radius are constant. However, the direction of the angular momentum vector changes as the body moves along the circular path.
D. Angular velocity of the body \( = \frac{v}{R} \): This is true. The angular velocity \( \omega \) is related to the linear velocity \( v \) and the radius \( R \) by the formula \( \omega = \frac{v}{R} \).
Thus, the correct answer is (3) A, B, and D only.
Step 3: Conclusion.
The correct answer is (3) A, B, and D only because all of these statements are true for uniform circular motion.