# 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 |
61%
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 |
72%
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. $$\theta = \tan^{-1}\left(\frac{1}{4}\right)$$
2. $$\theta = \tan^{-1}(4)$$
3. $$\theta = \tan^{-1}(2)$$
4. $$\theta = 45^{\circ}$$
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. $$7~\text{m/s}^2$$
2. $$\sqrt{7}~\text{m/s}^2$$
3. $$5~\text{m/s}^2$$
4. $$1~\text{m/s}^2$$

Subtopic:  Acceleration |
77%
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 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 |
85%
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.  $2\mathrm{mv}$

2.  $\mathrm{mv}/\sqrt{2}$

3.  $\mathrm{mv}\sqrt{2}$

4.  zero

Subtopic:  Projectile Motion |
56%
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 ($\sqrt{3}$, $$3).$$ 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 |
76%
From NCERT
AIPMT - 2007
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