# 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 with respect to the north is given by: 1. $$45^{\circ}$$ west of north 2. $$30^{\circ}$$ west of north 3. $$0^{\circ}$$ west of north 4. $$60^{\circ}$$ west of north

Subtopic:  Relative Motion |
71%
From NCERT
NEET - 2019
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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 the 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 |
79%
From NCERT
NEET - 2019
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A car turns at a constant speed on a circular track of radius $$100$$ m, taking $$62.8$$ s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

 1 $$0,~0$$ 2 $$0,~10$$ m/s 3 $$10$$ m/s, $$10$$ m/s 4 $$10$$ m/s, $$0$$
Subtopic:  Speed & Velocity |
82%
From NCERT
AIPMT - 2006
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For a projectile projected at angles (45°-θ) and (45°+θ), 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 |
87%
From NCERT
AIPMT - 2006
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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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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 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 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 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 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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