Question

A particle moving in a circular path, covers equal distances in equal intervals of time. Then the quantity associated with the particle that remains constant with time is

• A. displacement
• B. velocity
• C. speed
• D. acceleration
• E. linear momentum

Hint:

In uniform circular motion, speed is constant but velocity is not, because its direction changes continuously.

Answer 1

The Correct Option is C

Step 1: Understand the given condition.
The particle covers equal distances in equal intervals of time. This means the motion is uniform, i.e., the magnitude of velocity remains constant.

Step 2: Identify what remains constant in uniform motion.
If equal distances are covered in equal intervals of time, then:
\[ \text{Speed}=\frac{\text{distance}}{\text{time}} \] remains constant.

Step 3: Analyze circular motion.
In circular motion, even if speed is constant, the direction of motion changes continuously. Therefore, velocity is not constant because it depends on both magnitude and direction.

Step 4: Check displacement.
Displacement keeps changing in circular motion and does not remain constant.

Step 5: Check acceleration.
In circular motion, acceleration (centripetal acceleration) continuously changes direction, so it is not constant as a vector quantity.

Step 6: Check linear momentum.
Since velocity changes direction, linear momentum also changes direction and hence is not constant.

Step 7: State the final answer.
Thus, the only quantity that remains constant is:
\[ \boxed{\text{speed}} \] which matches option \((3)\).