A particle is executing uniform circular motion with velocity \(\vec v\) and acceleration \(\vec a.\) Which of the following is true?

1. | \(\vec v\) is a constant; \(\vec a\) is not a constant |

2. | \(\vec v\) is not a constant; \(\vec a\) is not a constant |

3. | \(\vec v\) is a constant; \(\vec a\) is a constant |

4. | \(\vec v\) is not a constant; \(\vec a\) is a constant |

Subtopic: Circular Motion |

53%

From NCERT

NEET - 2023

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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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In the given figure, \(a=15\) m/s^{2} represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:

1. \(4.5\) m/s

2. \(5.0\) m/s

3. \(5.7\) m/s

4. \(6.2\) m/s

Subtopic: Circular Motion |

61%

From NCERT

NEET - 2016

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A particle moves so that its position vector is given by, \(\vec{r}=\mathrm{cos} \omega t ~\hat{x}+ \mathrm{sin} \omega t~ \hat{y},\) where \(\omega\) is a constant. Which of the following is true?

1. | velocity and acceleration both are parallel to \(\vec{r}.\) |

2. | velocity is perpendicular to \(\vec{r}\) and acceleration is directed towards to origin. |

3. | velocity is parallel to \(\vec{r}\) and acceleration is directed away from the origin. |

4. | velocity and acceleration both are perpendicular to \(\vec{r}.\) |

Subtopic: Circular Motion |

78%

From NCERT

NEET - 2016

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A particle of mass \(10\) g moves along a circle of radius \(6.4\) cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to \(8 \times 10^{-4}\)^{ }J by the end of the second revolution after the beginning of the motion?

1. | \(0.15\) m/s^{2} |
2. | \(0.18\) m/s^{2} |

3. | \(0.2\) m/s^{2} |
4. | \(0.1\) m/s^{2} |

Subtopic: Circular Motion |

53%

From NCERT

NEET - 2016

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The position vector of a particle \(\vec{R}\) as a function of time \(t\) is given by;

\(\overrightarrow{\mathrm{R}}=4 \sin (2 \pi \mathrm{t}) \hat{\mathrm{i}}+4 \cos (2 \pi \mathrm{t}) \hat{\mathrm{j}}\)

Where \(R\) is in meters, \(t\) is in seconds and \(\mathrm{\hat{i},\hat{j}}\) denotes unit vectors along \(\mathrm{x}\) and \(\mathrm{y}\)-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

1. | acceleration is along \(-\overrightarrow{R}\). |

2. | magnitude of the acceleration vector is \(\frac{v^2}{R}\), where \(v\) is the velocity of the particle. |

3. | magnitude of the velocity of the particle is \(8\) m/s. |

4. | path of the particle is a circle of radius \(4\) m. |

Subtopic: Circular Motion |

60%

From NCERT

NEET - 2015

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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 particle moves in the \((x\text-y)\) plane according to the rule \(x = a sin (\omega t)\) and \(y = a cos (\omega t)\). The particle follows:

1. | a circular path. |

2. | a parabolic path. |

3. | a straight line path inclined equally to x and y-axes. |

4. | an elliptical path. |

Subtopic: Circular Motion |

76%

From NCERT

AIPMT - 2010

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

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

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

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

Subtopic: Circular Motion |

76%

From NCERT

AIPMT - 2005

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A particle moves along a circle of radius \({{20}\over{\pi}} m\) with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. 40 ms^{–2 }

2. 640π ms^{–2 }

3. 160π ms^{–2 }

4. 40π ms^{–2 }

Subtopic: Circular Motion |

56%

From NCERT

AIPMT - 2003

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