A swimmer can swim in still water at a speed of 5 m/s and takes t1 and t2, time to cross a river in the shortest time and shortest path respectively. If the speed of the river increases, the time is taken to cross the river in the shortest time and the shortest path be t'1 and t'2 respectively. Then

1.  t1 < t1', t2 < t2'

2.  t1 > t1', t2 > t2'

3.  t1 = t1', t2 < t2'

4.  t1 = t1', t2 > t2'

Subtopic:  Relative Motion |
 52%
From NCERT
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A sprinkler is deployed to irrigate the garden. The speed of water-jet from the sprinkler is u. The maximum area which can be irrigated by the sprinkler is

1.  π2u2g

2.  πu2g

3.  πu2g2

4.  πu4g2

Subtopic:  Projectile Motion |
 67%
From NCERT
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Which of the following is an appropriate expression for the radius of curvature of a projectile at the highest point? (R  Range of projectile)

(1) R2 cot θ

(2) R2 tan θ

(3) 2R cot θ

(4) 2R tan θ

Subtopic:  Projectile Motion |
From NCERT
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The coordinates of a particle moving in the x-y plane vary with time according to the following relation:

x = Bty = At.

The locus of the particle is:

(1) Parabola

(2) Circle

(3) Eclipse

(4) Hyperbola

Subtopic:  Position & Displacement |
From NCERT
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If t1 represents the instant at which the instantaneous velocity becomes perpendicular to the direction of initial velocity during a projectile and t2 represents the time after which the particle attains maximum height, then t1t2 is:

1.  ug

2.  2ug

3.  u2g

4.  u sin2 θg

Subtopic:  Projectile Motion |
From NCERT
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A park is in the shape of a regular hexagon. Six friends standing at each corner of the park start moving towards each other with the same speed 2 m/s and meet each other after 60 s. The side of the park is

(1) 120 m

(2) 30 m

(3) 240 m

(4) 60 m

Subtopic:  Relative Motion |
 52%
From NCERT
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A ball is projected horizontally from a cliff 40 m high at a speed of 40 m/s and simultaneously a ball is dropped. If the time taken by the two balls to reach the ground are t1 and t2 respectively (taking air friction into consideration), then

(1) t1 > t2

(2) t1 < t2

(3) t1 = t2

(4) Depending on air friction t1 maybe less or more than t2

Subtopic:  Projectile Motion |
 75%
From NCERT
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 Select the incorrect statement:

1. It is possible to have \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right|=0\) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}} \neq 0 \)
2. It is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0 \) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 .\)
3. it is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right|=0\) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 . \)
4. It is possible to have \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0\) \(\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}} \neq 0 \)

Subtopic:  Acceleration |
 56%
From NCERT
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A projectile is fired horizontally from the top of a tower. The time after which the instantaneous velocity will be perpendicular to the initial velocity is (neglect air resistance) :

(1) t = u sin θg

(2) t = ug sin θ

(3) t = ug cos θ

(4) It will never be perpendicular at any instant

Subtopic:  Projectile Motion |
From NCERT
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A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be: [assume the radius of the circle is 10/π2]
         

1. \(10 \sqrt{3} \) 2. \(20 \sqrt{3}\)
3. 10 4. 0
Subtopic:  Circular Motion |
From NCERT
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