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 |

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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 |

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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 |

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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 |

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A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi}$ sec. 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 |

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If the equation for the displacement of a particle moving on a circular path is given by $\left(\theta \right)=2{t}^{3}+0.5$, 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 |

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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 |

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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 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 |

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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. ${\pi}^{2}{\text{}\mathrm{ms}}^{-2}$ and direction along the tangent to the circle.

2. ${\pi}^{2}{\text{}\mathrm{ms}}^{-2}$ and direction along the radius towards the centre.

3. $\frac{{\pi}^{2}}{4}{\text{}\mathrm{ms}}^{-2}$ and direction along the radius towards the centre.

4. ${\pi}^{2}{\text{}\mathrm{ms}}^{-2}$ and direction along the radius away from the centre.

Subtopic: Circular Motion |

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

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