A particle moves in the x-y plane according to rule $\mathrm{x}=\mathrm{asin\omega t}$ and $\mathrm{y}=\mathrm{acos\omega t}$. The particle follows:

1. | an elliptical path. |

2. | a circular path. |

3. | a parabolic path. |

4. | a straight line path inclined equally to the x and y-axis. |

Subtopic: Circular Motion |

62%

From NCERT

NEET - 2010

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The magnitude of a vector $\overrightarrow{\mathrm{A}}$ is constant but it is changing its direction continuously. The angle between $\overrightarrow{\mathrm{A}}$ and $\frac{\mathrm{d}\overrightarrow{\mathrm{A}}}{\mathrm{dt}}$ is:

1. 180°

2. 120°

3. 90°

4. 0°

Subtopic: Circular Motion |

64%

From NCERT

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What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\) :

1. | \(6 \hat{i}+2 \hat{j}-3 \hat{k} \) |

2. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \) |

3. | \(4 \hat{i}-13 \hat{j}+6 \hat{k}\) |

4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |

Subtopic: Circular Motion |

85%

From NCERT

PMT - 2000

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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. θ_{1}

2. θ_{2}

3. 2θ_{1}

4. 2θ_{2}

Subtopic: Circular Motion |

84%

From NCERT

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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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If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where θ 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 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. $\sqrt{{\mathrm{K}}^{2}+{\left(\frac{{\mathrm{K}}^{2}{\mathrm{t}}^{2}}{\mathrm{r}}\right)}^{2}}$

2. 2K

3. K

4. $\sqrt{{\mathrm{K}}^{2}+{\mathrm{K}}^{2}{\mathrm{t}}^{2}}$

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

1. | parallel to the position vector. |

2. | at 60° 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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