# 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 $2\pi \mathrm{R.}$ 2. distance covered is 2R. 3. displacement is zero. 4. distance covered is zero.

Subtopic:  Position & Displacement |
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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 $120°$ 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 |
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A car with a vertical windshield moves in a rain storm at a speed of 40 km/hr. The rain drops fall vertically with a constant speed of 20 m/s. The angle at which raindrops strike the windshield is

1. ${\mathrm{tan}}^{-1}\frac{5}{9}$

2. ${\mathrm{tan}}^{-1}\frac{9}{5}$

3. ${\mathrm{tan}}^{-1}\frac{3}{2}$

4. ${\mathrm{tan}}^{-1}\frac{2}{3}$

Subtopic:  Relative Motion |
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A particle projected from origin moves in the x-y plane with a velocity $\stackrel{\to }{\mathrm{v}}=3\stackrel{^}{\mathrm{i}}+6\mathrm{x}\stackrel{^}{\mathrm{j}}$, where $\stackrel{^}{\mathrm{i}}$ and $\stackrel{^}{\mathrm{j}}$ are the unit vectors along the x and y-axis. The equation of path followed by the particle is:

1. $\mathrm{y}={\mathrm{x}}^{2}$

2. $\mathrm{y}=\frac{1}{{\mathrm{x}}^{2}}$

3. $\mathrm{y}=2{\mathrm{x}}^{2}$

4. $\mathrm{y}=\frac{1}{\mathrm{x}}$

Subtopic:  Speed & Velocity |
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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $\mathrm{y}=\left(4\mathrm{t}-2{\mathrm{t}}^{2}\right)\mathrm{m}$ and $\mathrm{x}=\left(3\mathrm{t}\right)$ metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is

1. $30°$

2. $37°$

3. $45°$

4. $60°$

Subtopic:  Projectile Motion |
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The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection (u). Its range on the horizontal plane is:

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

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

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

4. $\frac{{\mathrm{u}}^{2}}{2\mathrm{g}}$

Subtopic:  Projectile Motion |
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The equation of a projectile is $\mathrm{y}=\mathrm{ax}-{\mathrm{bx}}^{2}$. Its horizontal range is

1. $\frac{\mathrm{a}}{\mathrm{b}}$

2. $\frac{\mathrm{b}}{\mathrm{a}}$

3. $\mathrm{a}+\mathrm{b}$

4. $\mathrm{b}-\mathrm{a}$

Subtopic:  Projectile Motion |
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When a particle is projected at some angle to the horizontal, it has a range R and time of flight t1. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is t2, then

1. ${\mathrm{t}}_{1}+{\mathrm{t}}_{2}=\frac{2\mathrm{R}}{\mathrm{g}}$

2. ${\mathrm{t}}_{1}-{\mathrm{t}}_{2}=\frac{\mathrm{R}}{\mathrm{g}}$

3. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}=\frac{2\mathrm{R}}{\mathrm{g}}$

4. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}=\frac{\mathrm{R}}{\mathrm{g}}$

Subtopic:  Projectile Motion |
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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 |
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A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of  will be

1. 0

2. $\frac{1}{7}$

3. $\frac{2}{7}$

4. $\frac{1}{11}$

Subtopic:  Position & Displacement |
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