A car starts from rest and accelerates at $5\mathrm{m}/{\mathrm{s}}^{2}$. At t = 4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s?

(Take g = 10 m/s^{2})

1. $20\sqrt{2}\mathrm{m}/\mathrm{s},0\mathrm{m}/{\mathrm{s}}^{2}$

2. $20\sqrt{2}\mathrm{m}/\mathrm{s},10\mathrm{m}/{\mathrm{s}}^{2}$

3. $20\mathrm{m}/\mathrm{s},5\mathrm{m}/{\mathrm{s}}^{2}$

4. $20\mathrm{m}/\mathrm{s},0$

Subtopic: Projectile Motion |

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A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle $\text{'}\mathrm{\theta}\text{'}$ to the horizontal, the maximum height attained by it equals 4R. The angle of projection, $\mathrm{\theta}$, is then given by:

1. $\mathrm{\theta}={\mathrm{sin}}^{-1}{\left(\frac{{\mathrm{\pi}}^{2}\mathrm{R}}{{\mathrm{gT}}^{2}}\right)}^{1/2}$

2. $\mathrm{\theta}={\mathrm{sin}}^{-1}{\left(\frac{2{\mathrm{gT}}^{2}}{{\mathrm{\pi}}^{2}\mathrm{R}}\right)}^{1/2}$

3. $\mathrm{\theta}={\mathrm{cos}}^{-1}{\left(\frac{{\mathrm{gT}}^{2}}{{\mathrm{\pi}}^{2}\mathrm{R}}\right)}^{1/2}$

4. $\mathrm{\theta}={\mathrm{cos}}^{-1}{\left(\frac{{\mathrm{\pi}}^{2}\mathrm{R}}{{\mathrm{gT}}^{2}}\right)}^{1/2}$

Subtopic: Projectile Motion |

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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t north is given by:

1. 45$\xb0$ west of north

2. 30$\xb0$ west of north

3. 0$\xb0$ west of north

4. 60$\xb0$ west of north

Subtopic: Relative 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 particle starting from rest moves in a circle of radius 'r'. It attains a velocity of ${v}_{0}$ m/s on completion of n rounds. Its angular acceleration will be:

1. $\frac{{v}_{0}}{n}rad/{s}^{2}$

2. $\frac{{v}_{0}^{2}}{2{\mathrm{\pi nr}}^{2}}rad/{s}^{2}$

3. $\frac{{v}_{o}^{2}}{4{\mathrm{\pi nr}}^{2}}rad/{s}^{2}$

4. $\frac{{v}_{0}^{2}}{4\mathrm{\pi nr}}rad/{s}^{2}$

Subtopic: Circular Motion |

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Two bullets are fired horizontally and simultaneously towards each other from rooftops of two buildings (building being 100 m apart and being of the same height of 200 m) with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/${s}^{2}$)?

1. after 2s at a height of 180 m

2. after 2s at a height of 20 m

3. after 4s at a height of 120 m

4. they will not collide.

Subtopic: Relative Motion |

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The x and y coordinates of the particle at any time are $\mathrm{x}=5\mathrm{t}-2{\mathrm{t}}^{2}$ and y= 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t= 2sec is:

1. $5\hat{i}\mathrm{m}/{\mathrm{s}}^{2}$

2. $-4\hat{i}\mathrm{m}/{\mathrm{s}}^{2}$

3. $-8\hat{j}\mathrm{m}/{\mathrm{s}}^{2}$

4. 0

Subtopic: Acceleration |

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In the given figure, a = 15m /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 |

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

1. Velocity and acceleration both are parallel to $\overrightarrow{\mathrm{r}}$.

2. Velocity is perpendicular to $\overrightarrow{\mathrm{r}}$ and acceleration is directed towards to origin.

3. Velocity is parallel to $\overrightarrow{\mathrm{r}}$ and acceleration is directed away from the origin.

4. Velocity and acceleration both are perpendicular to $\overrightarrow{\mathrm{r}}$.

2. Velocity is perpendicular to $\overrightarrow{\mathrm{r}}$ and acceleration is directed towards to origin.

3. Velocity is parallel to $\overrightarrow{\mathrm{r}}$ and acceleration is directed away from the origin.

4. Velocity and acceleration both are perpendicular to $\overrightarrow{\mathrm{r}}$.

Subtopic: Circular Motion |

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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 x 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}

2. 0.18 m/s

3. 0.2 m/s

4. 0.1 m/s

Subtopic: Circular Motion |

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