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 |
 50%
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.\(\frac{\overrightarrow{r_1}-\overrightarrow{r_2}}{\left|\overrightarrow{r_1}-\overrightarrow{r_2}\right|}=\frac{\overrightarrow{v_2}-\overrightarrow{v_1}}{\left|\overrightarrow{v_2}-\overrightarrow{v_1}\right|}\)   
2. \(\overrightarrow{r_1} \cdot \overrightarrow{v_1}=\overrightarrow{r_2} \cdot \overrightarrow{v_2}\)   
3. \(\overrightarrow{r_1} \times \overrightarrow{v_1}=\overrightarrow{r_2} \times \overrightarrow{v_2}\)     
4. \(\overrightarrow{r_1}-\overrightarrow{r_2}=\overrightarrow{v_1}-\overrightarrow{v_2}\) 

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/s2
2. \(5.9\) m/s2
3. \(16.3\) m/s2
4. \(110.8\) m/s2

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 |
 84%
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. θ=tan-114
2. θ=tan-14
3. θ=tan-12
4. θ=450

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/s2 2. \(36\) m/s2
3. \(5\) m/s2 4. \(15\) m/s2
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. \( 7 \mathrm{~m} / \mathrm{s}^2 \)
2. \( \sqrt{7} \mathrm{~m} / \mathrm{s}^2 \)
3. \( 5 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1 \mathrm{~m} / \mathrm{s}^2\)

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/s2, 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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