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 |
55%
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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 |
71%
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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 |
76%
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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 |
68%
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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 |
84%
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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 |
69%
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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 |
57%
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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 |
66%
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