# Consider the motion of the tip of the second hand of a clock. In one minute (assuming $$R$$ to be the length of the second hand), its: 1. displacement is $$2\pi R$$ 2. distance covered is $$2R$$ 3. displacement is zero. 4. distance covered is zero.

Subtopic:  Position & Displacement |
86%
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A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of $$5$$ m/s at an angle of $$120^\circ$$ with the flow. The speed of the flow must be:
1. $$2.5$$ m/s
2. $$3$$ m/s
3. $$4$$ m/s
4. $$1.5$$ m/s

Subtopic:  Relative Motion |
83%
From NCERT
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When a particle is projected at some angle to the horizontal, it has a range $$R$$ and time of flight $$t_1$$. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is $$t_2$$, then:
1. $$t_{1} + t_{2} = \frac{2 R}{g}$$
2. $$t_{1} - t_{2} = \frac{R}{g}$$
3. $$t_{1} t_{2} = \frac{2 R}{g}$$
4. $$t_{1} t_{2} = \frac{R}{g}$$

Subtopic:  Projectile Motion |
74%
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A car is moving at a speed of $$40$$ m/s on a circular track of radius $$400$$ m. This speed is increasing at the rate of $$3$$ m/s2. The acceleration of the car is:
1. $$4$$ m/s2
2. $$7$$ m/s2
3. $$5$$ m/s2
4. $$3$$ m/s2

Subtopic:  Circular Motion |
75%
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A particle starts from the origin at $$t=0$$ sec with a velocity of $$10\hat j~\text{m/s}$$ and moves in the $$x\text-y$$ plane with a constant acceleration of $$(8.0\hat i +2.0 \hat j)~\text{m/s}^2$$. At what time is the $$x\text-$$coordinate of the particle $$16~\text{m}$$?
1. $$2$$ s
2. $$3$$ s
3. $$4$$ s
4. $$1$$ s

Subtopic:  Uniformly Accelerated Motion |
72%
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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%
From NCERT
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A cat is situated at point $$A$$ ($$0,3,4$$) and a rat is situated at point $$B$$ ($$5,3,-8$$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. $$5$$ unit
2. $$12$$ unit
3. $$13$$ unit
4. $$17$$ unit

Subtopic:  Position & Displacement |
75%
From NCERT
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Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

 1 The faster one 2 The slower one 3 Depends on masses 4 Both will reach simultaneously
Subtopic:  Projectile Motion |
76%
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A bus is going to the North at a speed of $$30$$ kmph. It makes a $$90^{\circ}$$ left turn without changing the speed. The change in the velocity of the bus is:

 1 $$30$$ kmph towards $$W$$ 2 $$30$$ kmph towards $$S\text-W$$ 3 $$42.4$$ kmph towards $$S\text-W$$ 4 $$42.4$$ kmph towards $$N\text-W$$
Subtopic:  Speed & Velocity |
58%
From NCERT
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A man can row a boat with a speed of $$10$$ kmph in still water. The river flows at $$6$$ kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width $$1$$ km is:
1. $$\frac{1}{8}~\text{h}$$
2. $$\frac{1}{4}~\text{h}$$
3. $$\frac{1}{2}~\text{h}$$
4. $$1~\text{h}$$

Subtopic:  Relative Motion |
72%
From NCERT
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