A particle moving with uniform speed in a circular path maintains:
1. constant acceleration.
2. constant velocity but varying acceleration.
3. varying velocity and varying acceleration.
4. constant velocity.
Subtopic:  Circular Motion |
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For a smoothly running analog clock, the ratio of the number of rotations made in a day by the hour hand to the second hand, respectively, is:
1. \(24 :1\)
2. \(1:720\)
3. \(1:60\)
4. \(2:5\)
Subtopic:  Circular Motion |
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A particle is executing uniform circular motion with velocity \(\vec v\) and acceleration \(\vec a.\) Which of the following is true?
1. \(\vec v\) is a constant; \(\vec a\) is not a constant.
2. \(\vec v\) is not a constant; \(\vec a\) is not a constant.
3. \(\vec v\) is a constant; \(\vec a\) is a constant.
4. \(\vec v\) is not a constant; \(\vec a\) is a constant.
Subtopic:  Circular Motion |
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Two particles \(A\) and \(B\) are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:

1. \( 1: 1 \) 2. \(r_A: r_B \)
3. \(v_A: v_B \) 4. \(r_B: r_A\)
Subtopic:  Circular Motion |
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In the given figure, \(a=15\) m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:

              

1. \(4.5\) m/s
2. \(5.0\) m/s
3. \(5.7\) m/s
4. \(6.2\) m/s

Subtopic:  Circular Motion |
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A particle moves so that its position vector is given by, \(\overrightarrow{r}=\cos \omega t ~\hat{x}+ \sin \omega t~ \hat{y},\) where \(\omega\) is a constant. Which of the following is true?
1. velocity and acceleration both are parallel to \(\overrightarrow{r}.\)
2. velocity is perpendicular to \(\overrightarrow{r}\) and acceleration is directed towards to origin.
3. velocity is parallel to \(\overrightarrow{r}\) and acceleration is directed away from the origin.
4. velocity and acceleration both are perpendicular to \(\overrightarrow{r}.\)
Subtopic:  Circular Motion |
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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 \(8 \times 10^{-4}\) 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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The position vector of a particle \(\vec{R }\) as a function of time \(t\) is given by:
\(\vec{{R}}=4 \sin (2 \pi {t}) \hat{i}+4 \cos (2 \pi {t}) \hat{j},\)
where \(R\) is in metres, \(t\) is in seconds and \({\hat{i},\hat{j}}\) denotes unit vectors along \({x}\) and \({y}\text-\)directions, respectively. Which one of the following statements is wrong for the motion of the particle?
1. Acceleration is along \((\text{-}\vec R )\).
2. Magnitude of the acceleration vector is \(\frac{v^2}{R}\), 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 \(4\) m.
Subtopic:  Circular Motion |
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A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. 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 particle moves in the \((x\text-y)\) plane according to the rule \(x = a \sin (\omega t)\) and \(y = a \cos (\omega t)\). The particle follows:

1. a circular path.
2. a parabolic path.
3. a straight line path inclined equally to x and y-axes.
4. an elliptical path.
Subtopic:  Circular Motion |
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