# A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8 x 10-4 J by the end of the second revolution after the beginning of the motion? 1. 0.15 m/s2 2. 0.18 m/s2 3. 0.2 m/s2 4. 0.1 m/s2

Subtopic:  Circular Motion |
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A ship A is moving Westwards with a speed of 10 kmph and a ship B 100 km South of A, is moving Northwards with a speed of 10 kmph. The time after which the distance between them becomes the shortest is:
1. 0 h
2. 5 h
3. $5\sqrt{2}$h
4. $10\sqrt{2}$h

Subtopic:  Relative Motion |
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Two particles A and B, move with constant velocities v1 and vrespectively. At the initial moment, their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision will be

1. $\frac{{\mathrm{r}}_{1}-{\mathrm{r}}_{2}}{\left|{\mathrm{r}}_{1}-{\mathrm{r}}_{2}\right|}=\frac{{\mathrm{v}}_{2}-{\mathrm{v}}_{1}}{\left|{\mathrm{v}}_{2}-{\mathrm{v}}_{1}\right|}$

2. ${\mathrm{r}}_{1}·{\mathrm{v}}_{1}={\mathrm{r}}_{2}·{\mathrm{v}}_{2}$

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

4. ${\mathrm{r}}_{1}-{\mathrm{r}}_{2}={\mathrm{v}}_{1}-{\mathrm{v}}_{2}$

Subtopic:  Relative Motion |
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The position vector of a particle R as a function of time t is given by
$\stackrel{\to }{\mathrm{R}}=4\mathrm{sin}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{i}}+4\mathrm{cos}\left[2\mathrm{\pi t}\right]\stackrel{^}{\mathrm{j}}$
Where R is in meters, t is in seconds and  denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

1. Acceleration is along $-\stackrel{\to }{\mathrm{R}}$.

2. Magnitude of the acceleration vector is $\frac{{\mathrm{v}}^{2}}{\mathrm{R}}$, where v is the velocity of the particle.

3. Magnitude of the velocity of the particle is 8 m/s.

4. Path of the particle is a circle of radius 4m.

Subtopic:  Circular Motion |
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A projectile is fired from the surface of the earth with a velocity of 5ms–1 and at an angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3ms–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the other planet is: (given g = 9.8 ms–2)

1. 3.5 m/s2

2. 5.9 m/s2

3. 16.3 m/s2

4. 110.8 m/s2

Subtopic:  Projectile Motion |
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The velocity of a projectile at the initial point A is $\left(2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}\right)$m/s. Its velocity (in m/s) at point B is: 1. $-2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}$

2. $2\stackrel{^}{\mathrm{i}}-3\stackrel{^}{\mathrm{j}}$

3. $2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}$

4. $-2\stackrel{^}{\mathrm{i}}-3\stackrel{^}{\mathrm{j}}$

Subtopic:  Projectile Motion |
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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1. $\theta ={\mathrm{tan}}^{-1}\left(\frac{1}{4}\right)$

2. $\theta ={\mathrm{tan}}^{-1}\left(4\right)$

3. $\theta ={\mathrm{tan}}^{-1}\left(2\right)$

4. $\theta ={45}^{0}$

Subtopic:  Projectile Motion |
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A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi }$ sec. The acceleration of the particle is:

1.  25 m/s2

2.  36 m/s2

3.  5 m/s2

4.  15 m/s2

Subtopic:  Circular Motion |
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A body is moving with a velocity of 30 m/s towards the east. After 10 sec, its velocity becomes 40 m/s towards the north. The average acceleration of the body is:

1.

2.

3.

4.

Subtopic:  Acceleration |
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A missile is fired for a maximum range with an initial velocity of 20 m/s. If g= 10 m/s2, then the range of the missile will be

1.  50 m

2.  60 m

3.  20 m

4.  40 m

Subtopic:  Projectile Motion |
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