Which one of the following statements is not true?

1. The magnitude of a vector is always a scalar.
2. The average speed of a particle is either greater or equal to the magnitude of the average velocity of the particle over the same interval of time.
3. Three vectors not lying in a plane can never add up to give a null vector.
4. Each component of a vector is always a scalar.

Subtopic:  Speed & Velocity |
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A cyclist starts from the center \(\mathrm{O}\) of a circular park of radius \(1\) km, reaches the edge \(\mathrm{P}\) of the park, then cycles along the circumference, and returns to the center along \(\mathrm{QO}\) as shown in the figure. If the round trip takes \(10\) min, then the average speed of the cyclist is:
      

1. \(22.42\) km/h
2. \(23.32\) km/h
3. \(21.42\) km/h
4. \(27.12\) km/h

Subtopic:  Speed & Velocity |
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A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). How much high above the ground, can the cricketer throw the same ball?
1. \(50~\text{m}\)
2. \(60~\text{m}\)
3. \(75~\text{m}\)
4. \(100~\text{m}\)

Subtopic:  Projectile Motion |
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An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Then the ratio of its centripetal acceleration with the acceleration due to gravity is:

1. 5.4:1
2. 6.4:1
3. 4:1
4. 1:1

Subtopic:  Circular Motion |
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Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

      

1. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)

Subtopic:  Position & Displacement |
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Rain is falling vertically with a speed of \(30\) m/s. A woman rides a bicycle with a speed of \(10\) m/s in the north to south direction. What is the direction in which she should hold her umbrella? [Given: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)

1. \(16^{\circ}\) with the vertical, towards north
2. \(18^{\circ}\) with the vertical, towards north
3. \(16^{\circ}\) with the vertical, towards south
4. \(18^{\circ}\) with the vertical, towards south
Subtopic:  Relative Motion |
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A man can swim at a speed of \(4.0\) km/h in still water. How long does he take to cross a river \(1.0\) km wide if the river flows steadily at \(3.0\) km/h and he makes his strokes normal to the river current? 
1. \(20\) min
2. \(18\) min
3. \(15\) min
4. \(16\) min

Subtopic:  Relative Motion |
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In a harbor, the wind is blowing at the speed of \(72~\text{km/h}\), and the flag on the mast of a boat anchored in the harbor flutters along the \(\mathrm{N\text-E}\) direction. If the boat starts moving at a speed of \(51~\text{km/h}\) to the north, what is the direction of the flag on the mast of the boat?

1. almost due north
2. almost due east
3. almost due west
4. almost due south
Subtopic:  Relative Motion |
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The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall?

1. 150.5 m
2. 165.6 m
3. 145.3 m
4. 158.2 m

Subtopic:  Projectile Motion |
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A stone tied to the end of a string \(80\) cm long is whirled in a horizontal circle at a constant speed. If the stone makes \(14\) revolutions in \(25\) s, what is the magnitude of the acceleration of the stone?

1. \(8.1\) ms–2 2. \(7.7\) ms–2
3. \(8.7\) ms–2 4. \(9.9\) ms–2
Subtopic:  Circular Motion |
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