The position vector of a particle R as a function of time t is given by 
R=4sin2πti^+4cos2πtj^
Where R is in meters, t is in seconds and i^, j^ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

1. Acceleration is along -R.

2. Magnitude of the acceleration vector is v2R, 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 4m.

Subtopic:  Circular Motion |
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A projectile is fired from the surface of the earth with a velocity of 5ms–1 and at an angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3ms–1 at the same angle follows a trajectory which is identical with 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 |
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The velocity of a projectile at the initial point A is 2i^+3j^m/s. Its velocity (in m/s) at point B is:
            

1. -2i^+3j^

2. 2i^-3j^

3. 2i^+3j^

4. -2i^-3j^

Subtopic:  Projectile Motion |
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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. θ=tan-114

2. θ=tan-14

3. θ=tan-12

4. θ=450

 

Subtopic:  Projectile Motion |
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A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π 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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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.  7 m/s2

2.  7 m/s2

3.  5 m/s2

4.  1 m/s2

Subtopic:  Acceleration |
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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 particle has initial velocity (3i^ + 4j^) and has acceleration (0.4i^+ 0.3j^). Its speed after 10 s is

1. 7 units

2. 72units

3. 8.5 units

4. 10 units

Subtopic:  Uniformly Accelerated Motion |
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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.  2mv

2.  mv/2

3.  mv2

4.  zero

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 (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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