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Q. No.Two particles are moving along the same circular path. If the ratio of their centripetal accelerations is \(3:4,\) then the ratio of their tangential velocities is:
| 1. | \(2:\sqrt3\) | 2. | \(\sqrt3:2 \) |
| 3. | \(\sqrt3:1\) | 4. | \(1:\sqrt{3}\) |
Subtopic: Â Circular Motion |
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A particle moving in a uniform circular motion of radius \(1\) m has velocity \(3 \hat j ~\text {m/s}\) at point \(B.\) What are the velocity \((\vec{v})\)and acceleration \((\vec{a})\) at diametrically opposite point \(A?\)
| 1. | \( \vec{v}_A=3 \hat{j}~\text{m/s} ;~\vec{a}_A=-9 \hat{i}~\text{m/s}^2\) |
| 2. | \( \vec{v}_A=-3 \hat{j}~\text{m/s};~\vec{a}_A=9 \hat{i}~\text{m/s}^2\) |
| 3. | \(\vec{v}_A=-3 \hat{i}~~\text{m/s};\vec{a}_A=9 \hat{j}~\text{m/s}^2\) |
| 4. | \(\vec{v}_A=3 \hat{i}~\text{m/s} ;~\vec{a}_A=9 \hat{j}~\text{m/s}^2 \) |
Subtopic: Â Circular Motion |
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Level 1: 80%+
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A particle is in a uniform circular motion with a time period of \(4~\mathrm{s}\) and radius \(\sqrt{2}~\mathrm{m}\). What is the magnitude of displacement in \(3~\mathrm{s}\)?
1. \(4~\mathrm{m}\)
2. \(3~\mathrm{m}\)
3. \(2~\mathrm{m}\)
4. \(1~\mathrm{m}\)
1. \(4~\mathrm{m}\)
2. \(3~\mathrm{m}\)
3. \(2~\mathrm{m}\)
4. \(1~\mathrm{m}\)
Subtopic: Â Circular Motion |
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Level 2: 60%+
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The motion of a particle in the \(xy \text-\)plane is described by the following equations:
\(x=4 \sin \left(\dfrac{\pi}{2}-\omega t\right)~ \text m,\) \(y=4 \sin \left(\omega t\right) ~\text m.\)
Which of the following best describes the path traced by the particle?
\(x=4 \sin \left(\dfrac{\pi}{2}-\omega t\right)~ \text m,\) \(y=4 \sin \left(\omega t\right) ~\text m.\)
Which of the following best describes the path traced by the particle?
| 1. | circular | 2. | helical |
| 3. | parabolic | 4. | elliptical |
Subtopic: Â Circular Motion |
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For a particle in a uniform circular motion, the acceleration \(\vec a\) at any point P(R, \(\theta\)) on the circular path of radius R is: (when \(\theta\) is measured from the positive x-axis and v is uniform speed):
1. \(-\frac{v^2}{R} \sin \theta \hat{i}+\frac{v^2}{R} \cos \theta \hat{j} \)
2. \(-\frac{v^2}{R} \cos \theta \hat{i}+\frac{v^2}{R} \sin \theta \hat{j} \)
3. \(-\frac{v^2}{R} \cos \theta \hat{i}-\frac{v^2}{R} \sin \theta \hat{j} \)
4. \(-\frac{v^2}{R} \hat{i}+\frac{v^2}{R} \hat{j}\)
1. \(-\frac{v^2}{R} \sin \theta \hat{i}+\frac{v^2}{R} \cos \theta \hat{j} \)
2. \(-\frac{v^2}{R} \cos \theta \hat{i}+\frac{v^2}{R} \sin \theta \hat{j} \)
3. \(-\frac{v^2}{R} \cos \theta \hat{i}-\frac{v^2}{R} \sin \theta \hat{j} \)
4. \(-\frac{v^2}{R} \hat{i}+\frac{v^2}{R} \hat{j}\)
Subtopic: Â Circular Motion |
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Level 3: 35%-60%
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A particle moves at a constant speed along the circumference of a circle with a radius \(R,\) subject to a central fictitious force \(F\) that is inversely proportional to \(R^3.\) Its time period of revolution will be given by:
| 1. | \( T \propto R^2 \) | 2. | \( T \propto R^{\frac{3}{2}} \) |
| 3. | \( T \propto R^{\frac{5}{2}} \) | 4. | \(T \propto R^{\frac{4}{3}} \) |
Subtopic: Â Circular Motion |
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A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \({x}\) distance more than the tip of minute hand. The value of \(\mathrm{x}\) in meter is nearly (Take \(\pi=3.14\) ) :
1. \(118.9\)
2. \(220.0\)
3. \(139.4\)
4. \(140.5\)
1. \(118.9\)
2. \(220.0\)
3. \(139.4\)
4. \(140.5\)
Subtopic: Â Circular Motion |
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A clock has a continuously moving second's hand of \(0.1~\text{m}\) length. The average acceleration of the tip of the second hand (in units of ms-2) is of the order of:
1. \(10^{-3}\)
2. \(10^{-4}\)
3. \(10^{-1}\)
4. \(10^{-2}\)
Subtopic: Â Circular Motion |
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