The angle turned by a body undergoing circular motion depends on the time as given by the equation, \(\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}\). It can be deduced that the angular acceleration of the body is?

1. \(\theta_1\)

2. \(\theta_2\)

3. \(2\theta_1\)

4. \(2\theta_2\)

Subtopic: Circular Motion |

84%

From NCERT

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If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:

1. \(8\) rad/sec

2. \(12\) rad/sec

3. \(24\) rad/sec

4. \(36\) rad/sec

Subtopic: Circular Motion |

81%

From NCERT

AIIMS - 1998

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A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

1. | \(25\) m/s^{2} |
2. | \(36\) m/s^{2} |

3. | \(5\) m/s^{2} |
4. | \(15\) m/s^{2} |

Subtopic: Circular Motion |

80%

From NCERT

AIPMT - 2011

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A car moves on a circular path such that its speed is given by \(v= Kt\), where \(K\) = constant and \(t\) is time. Also given: radius of the circular path is \(r\). The net acceleration of the car at time \(t\) will be:

1. \(\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}\)

2. \(2K\)

3. \(K\)

4. \(\sqrt{K^{2} + K^{2} t^{2}}\)

Subtopic: Circular Motion |

80%

From NCERT

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Two particles \(A\) and \(B\) are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:

1. \( 1: 1 \)

2. \(r_A: r_B \)

3. \(v_A: v_B \)

4. \(r_B: r_A\)

Subtopic: Circular Motion |

79%

From NCERT

NEET - 2019

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The position vector of a particle is \(\overrightarrow{r}= a \sin\omega t\hat i + a\cos \omega t\hat j\). The velocity of the particle is:

1. | parallel to the position vector. |

2. | at \(60^{\circ}\) with position vector. |

3. | parallel to the acceleration vector. |

4. | perpendicular to the position vector. |

Subtopic: Circular Motion |

79%

From NCERT

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A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?

1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |

3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |

Subtopic: Circular Motion |

78%

From NCERT

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If a particle is moving in a circular orbit with constant speed, then:

1. | its velocity is variable. |

2. | its acceleration is variable. |

3. | its angular momentum is constant. |

4. | All of the above |

Subtopic: Circular Motion |

78%

From NCERT

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A stone tied to the end of a \(1\) m long string is whirled in a horizontal circle at a constant speed. If the stone makes \(22\) revolutions in \(44\) seconds, what is the magnitude and direction of acceleration of the stone?

1. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the tangent to the circle. |

2. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the radius towards the centre. |

3. | \(\frac{\pi^2}{4}~\text{ms}^{-2} \) and direction along the radius towards the centre. |

4. | \(\pi^2~\text{ms}^{-2} \) and direction along the radius away from the centre. |

Subtopic: Circular Motion |

77%

From NCERT

AIPMT - 2005

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In a uniform circular motion, if the speed of the particle is \(2\) m/s and radius of the circle is \(2\) m, then the values of centripetal and tangential acceleration are, respectively:

1. \(2~\text{m/s}^2,~2~\text{m/s}^2\)

2. \(2~\text{m/s}^2,~1~\text{m/s}^2\)

3. \(0,~2~\text{m/s}^2\)

4. \(2~\text{m/s}^2,~0\)

Subtopic: Circular Motion |

75%

From NCERT

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