# A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:           1. $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2. $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3. $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4. $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 

Subtopic:  Position & Displacement |
74%
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Two particles move from A to C and A to D on a circle of radius R and diameter AB. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:

1. 2

2.  $2\sqrt{3}$

3.  $\sqrt{3}$

4.  $\frac{\sqrt{3}}{2}$

Subtopic:  Speed & Velocity |
62%
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A particle moves on the curve ${\mathrm{}}^{}$$$x^2 = 2y$$$\mathrm{}$. The angle of its velocity vector with the x-axis at the point $$\left(1, \frac{1}{2}\right )$$ will be:

 1 $$30^\circ$$ 2 $$60^\circ$$ 3 $$45^\circ$$ 4 $$75^\circ$$
Subtopic:  Speed & Velocity |
61%
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A particle is moving along a curve. Select the correct statement.

 1 If its speed is constant, then it has no acceleration. 2 If its speed is increasing, then the acceleration of the particle is along its direction of motion. 3 If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. 4 If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
68%
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A car is moving along east at 10 m/s and a bus is moving along north at 10 m/s. The velocity of the car with respect to the bus is along:

 1 North-East 2 South-East 3 North-West 4 South-West
Subtopic:  Relative Motion |
59%
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A particle starts moving from the origin in the XY plane and its velocity after time $$t$$ is given by $$\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}$$. The trajectory of the particle is correctly shown in the figure:

 1 2 3 4
Subtopic:  Speed & Velocity |
60%
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A particle is moving in the XY plane such that $$x = \left(t^2 -2t\right)$$ m, and $$y = \left(2t^2-t\right)$$ m, then:

 1 Acceleration is zero at t = 1 sec 2 Speed is zero at t = 0 sec 3 Acceleration is always zero 4 Speed is 3 m/s at t = 1 sec
Subtopic:  Acceleration |
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It is raining at 20 m/s in still air. Now a wind starts blowing with speed 10 m/s in the north direction. If a cyclist starts moving at 10 m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be

1. 20 m/s

2. $20\sqrt{2}$ m/s

3. $10\sqrt{5}$ m/s

4. 30 m/s

Subtopic:  Relative Motion |
52%
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River of width 500 m is flowing at a speed of 10 m/s. A swimmer can swim at a speed of 10 m/s in still water. If he starts swimming at an angle of 120° with the flow direction, then the distance he travels along the river while crossing the river is:

1. 250 m

2. $500\sqrt{3}$ m

3. $\frac{500}{\sqrt{3}}$ m

4. 500 m

Subtopic:  Relative Motion |
56%
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Path of a projectile with respect to another projectile so long as both remain in the air is:

1. Circular

2. Parabolic

3. Straight

4. Hyperbolic

Subtopic:  Projectile Motion |
67%
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