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A ship \(A\) is moving westward with a speed of \(10\) kmph and a ship \(B\), \(100 ~\text{km}\) South of \(A\), is moving northward with a speed of \(10\) \(\text{kmph}\). The time after which the distance between them becomes the shortest is:

1. \(0\) h

2. \(5\) h

3. \(5\sqrt{2}\) h

4. \(10\sqrt{2}\) h

Subtopic: Relative Motion |

From NCERT

NEET - 2015

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Two particles \(\mathrm{A}\) and \(\mathrm{B}\), move with constant velocities \(\overrightarrow{{v}_1}\) and \(\overrightarrow{{v}_2}\)_{ }respectively. At the initial moment, their position vectors are \(\overrightarrow{{r}_1}\) and \(\overrightarrow{{r}_2}\) respectively. The condition for particles \(\mathrm{A}\) and \(\mathrm{B}\) for their collision will be:

1.\(\dfrac{\vec{r_1}-\vec{r_2}}{\left|\vec{r_1}-\vec{r_2}\right|}=\dfrac{\vec{v_2}-\vec{v_1}}{\left|\vec{v_2}-\vec{v_1}\right|}\)

2. \(\vec{r_1} \cdot \vec{v_1}=\vec{r_2} \cdot \vec{v_2}\) ${\mathrm{}}_{}$

3. \(\vec{r_1} \times \vec{v_1}=\vec{r_2} \times \vec{v_2}\)${\mathrm{}}_{}$

4. \(\vec{r_1}-\vec{r_2}=\vec{v_1}-\vec{v_2}\)

Subtopic: Relative Motion |

69%

From NCERT

NEET - 2015

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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 projectile is fired from the surface of the earth with a velocity of \(5\) ms^{–1} and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3\) ms^{–1} at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given \(g=9.8\) ms^{–2})

1. \(3.5\) m/s^{2}

2. \(5.9\) m/s^{2}

3. \(16.3\) m/s^{2}

4. \(110.8\) m/s^{2}

Subtopic: Projectile Motion |

71%

From NCERT

AIPMT - 2014

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The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:

1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |

3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |

Subtopic: Projectile Motion |

83%

From NCERT

AIPMT - 2013

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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1. $\theta ={\mathrm{tan}}^{-1}\left(\frac{1}{4}\right)$

2. $\theta ={\mathrm{tan}}^{-1}\left(4\right)$

3. $\theta ={\mathrm{tan}}^{-1}\left(2\right)$

4. $\theta ={45}^{0}$

Subtopic: Projectile Motion |

75%

From NCERT

AIPMT - 2012

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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 body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) m/s towards the north. The average acceleration of the body is:

1. \( 7~\text{m/s}^2\)

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

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

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

Subtopic: Acceleration |

76%

From NCERT

AIPMT - 2011

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A missile is fired for a maximum range with an initial velocity of \(20\) m/s. If \(g=10\) m/s^{2}, then the range of the missile will be:

1. \(50\) m

2. \(60\) m

3. \(20\) m

4. \(40\) m

Subtopic: Projectile Motion |

83%

From NCERT

AIPMT - 2011

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A projectile is fired at an angle of \(45^\circ\) with the horizontal. The elevation angle \(\alpha\) of the projectile at its highest point, as seen from the point of projection is:

1. \(60^\circ\)

2. \(tan^{-1}\left ( \frac{1}{2} \right )\)

3. \(tan^{-1}\left ( \frac{\sqrt{3}}{2} \right )\)

4. \(45^\circ\)

Subtopic: Projectile Motion |

From NCERT

AIPMT - 2011

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