# A particle starting from the point (1, 2) moves in a straight line in the XY plane. Its coordinates at a later time are (2, 3). The path of the particle makes, with the x-axis, an angle of 1. 30°  2. 45° 3. 60°  4. data insufficient

Subtopic:  Position & Displacement |
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A particle is projected from a horizontal plane (x-z plane) such that its velocity vector at time t is given by $\stackrel{\to }{\mathrm{v}}=a\stackrel{^}{i}+\left(b-ct\right)\stackrel{^}{j}$. Its range on this horizontal plane is given by

1. $\frac{\mathrm{ba}}{\mathrm{c}}$

2. $\frac{2\mathrm{ba}}{\mathrm{c}}$

3. $\frac{3\mathrm{ba}}{\mathrm{c}}$

4. None

Subtopic:  Projectile Motion |
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A man is walking on the road with a speed 3 m/s. Rain is falling vertically at speed 3 m/s. At what angle from
the vertical, man has to hold his umbrella to avoid the rain drops?
1. ${45}^{\mathrm{o}}$

2. 30o

3. 60o

4. 90o

Subtopic:  Relative Motion |
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A river is 1 km wide. The banks are straight and parallel. The current is 5 km/h and is parallel to the banks. A boat has a maximum speed of 3 km/h in still water. In what direction should the boat head so as to arrive at point B directly opposite to its starting point A?

1. directly across the river

2. head $53°$ upstream from the line AB

4. the trip from A to B is not possible with this speed

Subtopic:  Relative Motion |
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Two particles A and B, move with constant velocities $$\vec{v_1}$$   and  $$\vec{v_2}$$ . At the initial moment their position vector are  $$\vec{r_1}$$ and  $$\vec{r_2}$$  respectively. The condition for particles A and B for their collision to happen will be

1.

2.

3.

4.

Subtopic:  Speed & Velocity |
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A particle moves along a parabolic path y = 9x2 in such a way that the x component of the velocity remains constant and has a value of . It can be deduced that the acceleration of the particle will be

1.

2.

3.

4.

Subtopic:  Acceleration |
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Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are  respectively, then: 1. ${\mathrm{v}}_{1}>{\mathrm{v}}_{2}>{\mathrm{v}}_{3}$

2. ${\mathrm{v}}_{3}>{\mathrm{v}}_{2}={\mathrm{v}}_{1}$

3. ${\mathrm{v}}_{1}={\mathrm{v}}_{2}={\mathrm{v}}_{3}$

4. ${\mathrm{v}}_{1}<{\mathrm{v}}_{2}<{\mathrm{v}}_{3}$

Subtopic:  Projectile Motion |
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Figure below shows a body of mass M moving with a uniform speed v on a circular path of radius, R. What is the change in acceleration in going from P1 to P2 1. zero

2. ${\mathrm{v}}^{2}/2\mathrm{R}$

3. $2{\mathrm{v}}^{2}/\mathrm{R}$

4. $\frac{{\mathrm{v}}^{2}}{\mathrm{R}}×\sqrt{2}$

Subtopic:  Circular Motion |
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A particle is projected with a speed u at an angle $\mathrm{\theta }$ to the horizontal. Radius of curvature at highest point of its trajectory is

1. $\frac{{\mathrm{u}}^{2}{\mathrm{cos}}^{2}\mathrm{\theta }}{2\mathrm{g}}$

2. $\frac{\sqrt{3}{\mathrm{u}}^{2}{\mathrm{cos}}^{2}\mathrm{\theta }}{2\mathrm{g}}$

3. $\frac{{\mathrm{u}}^{2}{\mathrm{cos}}^{2}\mathrm{\theta }}{\mathrm{g}}$

4. $\frac{\sqrt{3}{\mathrm{u}}^{2}{\mathrm{cos}}^{2}\mathrm{\theta }}{\mathrm{g}}$

Subtopic:  Circular Motion |
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii  with speeds  respectively. Their time periods of rotation are the same. The ratio of angular speed of A  to that of B will be:

1. 1: 1

2.

3.

4.

Subtopic:  Circular Motion |
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