A particle moves in the x-y plane according to rule x=asinωt and y=acosωt. The particle follows:

1. an elliptical path.
2. a circular path.
3. a parabolic path.
4. a straight line path inclined equally to the x and y-axis.

Subtopic:  Circular Motion |
 62%
From NCERT
NEET - 2010
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A particle has an initial velocity (\(2\mathrm{i}+3\mathrm{j}\)) and an acceleration (\(0.3\mathrm{i}+0.2\mathrm{j}\)). The magnitude of velocity after 10 s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)

Subtopic:  Uniformly Accelerated Motion |
 88%
From NCERT
NEET - 2012
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A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant.  Based on the information given, which of the following is true?

1. Velocity and acceleration, both are parallel to r.
2. Velocity is perpendicular to r and acceleration is directed towards the origin.
3. Velocity is not perpendicular to r and acceleration is directed away from the origin.
4. Velocity and acceleration, both are perpendicular to r.

Subtopic:  Acceleration |
 70%
From NCERT
NEET - 2016
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Two particles having position vectors r1=(3i^+5j^) metres and r2=(5i^3j^) metres are moving with velocities v1=(4i^+3j^) m/s and v2=(α i^+7j^) m/s. If they collide after 2 seconds, the value of ‘α’ is-

1. 2 2. 4
3. 6 4. 8
Subtopic:  Relative Motion |
 51%
From NCERT
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A steam boat goes across a lake and comes back (a) On a quiet day when the water is still and (b) On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both the days was the same, in which case will the steam boat complete the journey in lesser time:

1. Case (a)

2. Case (b)

3. Same in both case

4. Nothing can be predicted based on given data

Subtopic:  Relative Motion |
From NCERT
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A man sitting in a bus travelling in a direction from west to east with a speed of 40 km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear 

1. To fall vertically downwards

2. To fall at an angle going from west to east

3. To fall at an angle going from east to west

4. The information given is insufficient to decide the direction of the rain

Subtopic:  Relative Motion |
 53%
From NCERT
PMT - 1999
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A river is flowing from east to west at a speed of 5 m/min. A man on south bank of river, capable of swimming 10m/min in still water, wants to swim across the river in shortest time. He should swim:

1. Due north

2. Due north-east

3. Due north-east with double the speed of the river

4. None of the above

Subtopic:  Relative Motion |
 58%
From NCERT
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A boat is moving with a velocity 3i + 4j with respect to ground. The water in the river is moving with a velocity – 3i – 4j with respect to ground. The relative velocity of the boat with respect to water is 

1. 8j

2. – 6i – 8j

3. 6i +8j

4. 52

Subtopic:  Relative Motion |
 83%
From NCERT
PMT - 1998
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The horizontal range of a projectile is 43 times its maximum height. Its angle of projection will be:

1. 45°

2. 60°

3. 90°

4. 30°

Subtopic:  Projectile Motion |
 74%
From NCERT
PMT - 2003
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A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is 

1. 100 m

2. 80 m

3. 60 m

4. 50 m

Subtopic:  Projectile Motion |
 75%
From NCERT
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