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 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 |
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii  with speeds  respectively. Their time periods of rotation are the same. The ratio of angular speed of A  to that of B will be:

1. 1: 1

2.

3.

4.

Subtopic:  Circular Motion |
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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 |
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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 |
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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. 30o

2. 45o

3. 60o

4. 0o

Subtopic:  Position & Displacement |
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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 the 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 |
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A particle has initial velocity and has acceleration . 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 |
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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 |
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A body is moving with a velocity of 30 m/s towards the east. After 10 sec, its velocity becomes 40 m/s towards the north. The average acceleration of the body is:

1.

2.

3.

4.

Subtopic:  Acceleration |
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A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi }$ sec. 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 |
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