Two particles \({A}\) and \({B}\), move with constant velocities \(\vec{v}_1\) and \(\vec{v}_2\) respectively. At the initial moment, their position vectors are \(\vec{r}_1\) and \(\vec r_2\) respectively. The conditions for particles \({A}\) and \({B}\) 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. \(\vec{r}_1 \cdot \vec{v}_1=\vec{r}_2 \cdot \vec{v}_2\)
3. \(\vec{r}_1 \times \vec{v}_1=\vec{r}_2 \times \vec{v}_2\)
4. \(\vec{r}_1-\vec{r}_2=\vec{v}_1-\vec{v}_2\)

Subtopic:  Relative Motion |
 71%
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:
\(\vec{{R}}=4 \sin (2 \pi {t}) \hat{i}+4 \cos (2 \pi {t}) \hat{j},\)
where \(R\) is in metres, \(t\) is in seconds and \({\hat{i},\hat{j}}\) denotes unit vectors along \({x}\) and \({y}\text-\)directions, respectively. Which one of the following statements is wrong for the motion of the particle?
1. Acceleration is along \((\text{-}\vec R )\).
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 |
 62%
From NCERT
NEET - 2015
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The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the 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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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 |
 81%
From NCERT
AIPMT - 2011
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A missile is fired for a maximum range with an initial velocity of \(20~\text {m/s}.\) If \(g=10~\text{m/s}^2,\) then the range of the missile will be:

1. \(50~\text m\) 2. \(60~\text m\)
3. \(20~\text m\) 4. \(40~\text m\)
Subtopic:  Projectile Motion |
 84%
From NCERT
AIPMT - 2011
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A particle has initial velocity \((3\hat{i}+4\hat{j})\) and has acceleration \((0.4\hat{i}+0.3\hat{j}).\) Its speed after \(10\) s is:
1. \(7\) units
2. \(7\sqrt{2}\) units
3. \(8.5\) units
4. \(10\) units
Subtopic:  Uniformly Accelerated Motion |
 86%
From NCERT
AIPMT - 2010
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A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:

1.  2mv

2.  mv/2

3.  mv2

4.  zero

Subtopic:  Projectile Motion |
 57%
From NCERT
AIPMT - 2008
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A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are (3, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

Subtopic:  Position & Displacement |
 77%
From NCERT
AIPMT - 2007
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For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)

Subtopic:  Projectile Motion |
 88%
From NCERT
AIPMT - 2006
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A car turns at a constant speed on a circular track of radius \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

1. \(0,~0\) 2. \(0,\)  \(10~\text{m/s},\)
3. \(10~\text{m/s},\) ​​​​​​​ \(10~\text{m/s},\) 4. \(10~\text{m/s},\) \(0\)
Subtopic:  Speed & Velocity |
 83%
From NCERT
AIPMT - 2006
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