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A particle is revolving in a circle with...

A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant ?

A

Centripetal acceleration

B

Tangential acceleration

C

Angular acceleration

D

None of these

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The correct Answer is:
To solve the question, "A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant?" we will analyze the different types of acceleration involved in circular motion and determine which one remains constant. ### Step-by-Step Solution: 1. **Understanding Circular Motion**: - A particle moving in a circle experiences centripetal acceleration directed towards the center of the circle and tangential acceleration directed along the tangent to the circle. 2. **Centripetal Acceleration**: - The formula for centripetal acceleration (\(a_c\)) is given by: \[ a_c = \frac{v^2}{R} \] where \(v\) is the linear speed of the particle and \(R\) is the radius of the circle. - Since the speed \(v\) is increasing uniformly, \(a_c\) will also increase as \(v\) increases. Therefore, centripetal acceleration is **not constant**. 3. **Tangential Acceleration**: - Tangential acceleration (\(a_t\)) is related to the change in speed along the circular path. It can be expressed as: \[ a_t = \alpha \cdot R \] where \(\alpha\) is the angular acceleration. - Since the speed is increasing uniformly, \(a_t\) will also change as the speed changes. Thus, tangential acceleration is **not constant**. 4. **Angular Acceleration**: - Angular acceleration (\(\alpha\)) is defined as the rate of change of angular velocity (\(\omega\)) with respect to time: \[ \alpha = \frac{d\omega}{dt} \] - Given that the speed is increasing uniformly, the angular velocity \(\omega\) also increases uniformly. Therefore, \(\alpha\) remains constant. 5. **Conclusion**: - Among the options provided, the only acceleration that remains constant is the **angular acceleration** (\(\alpha\)). Thus, the correct answer is option 3. ### Final Answer: **Angular acceleration is constant.** ---

To solve the question, "A particle is revolving in a circle with increasing its speed uniformly. Which of the following is constant?" we will analyze the different types of acceleration involved in circular motion and determine which one remains constant. ### Step-by-Step Solution: 1. **Understanding Circular Motion**: - A particle moving in a circle experiences centripetal acceleration directed towards the center of the circle and tangential acceleration directed along the tangent to the circle. 2. **Centripetal Acceleration**: ...
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Knowledge Check

  • A particle is moving in a circle with uniform speed. IT has constant

    A
    velocity
    B
    Acceleration
    C
    kinetic energy
    D
    displacement
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