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

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 |

86%

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. \(\theta_1\)

2. \(\theta_2\)

3. \(2\theta_1\)

4. \(2\theta_2\)

Subtopic: Circular Motion |

84%

From NCERT

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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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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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The position vector of a particle is \(\vec{r}= a \sin\omega t \hat{i} + a\cos \omega t \hat{j}\). 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 |

80%

From NCERT

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A car is moving at a speed of \(40\) m/s on a circular track of radius \(400\) m. This speed is increasing at the rate of \(3\) m/s^{2}. The acceleration of the car is:

1. \(4\) m/s^{2}

2. \(7\) m/s^{2}

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

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

Subtopic: Circular Motion |

75%

From NCERT

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Certain neutron stars are believed to be rotating at about \(1\) rev/s. If such a star has a radius of \(20\) km, the acceleration of an object on the equator of the star will be:

1. | \(20 \times 10^8 ~\text{m/s}^2\) | 2. | \(8 \times 10^5 ~\text{m/s}^2\) |

3. | \(120 \times 10^5 ~\text{m/s}^2\) | 4. | \(4 \times 10^8 ~\text{m/s}^2\) |

Subtopic: Circular Motion |

70%

From NCERT

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A particle moves with constant speed *\(v\)* along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:

1. \(2\pi v / T\)

2. \(2\pi r / T\)

3. \(2\pi r^2 / T\)

4. \(2\pi v^2 / T\)

Subtopic: Circular Motion |

62%

From NCERT

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