Q. No.A car moving with a speed of \(54~\text{km/h}\) takes a turn of radius \(20~\text{m}\). A simple pendulum is suspended from the ceiling of the car. Determined the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10~\text{m/s}^2\))
1. \(\tan ^{-1}(0.5)\)
2. \(\tan ^{-1}(0.75)\)
3. \(\tan ^{-1}(1.125)\)
4. \(\tan ^{-1}(0.25)\)
1. \(\tan ^{-1}(0.5)\)
2. \(\tan ^{-1}(0.75)\)
3. \(\tan ^{-1}(1.125)\)
4. \(\tan ^{-1}(0.25)\)
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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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 moves along a circular path of radius \(9~\text{m}\) and completes \(120\) revolutions in \(3\) minutes. What is the centripetal acceleration of the particle?
| 1. | \(8 \pi^2 ~\text{m/s}^2\) | 2. | \(16 \pi^2~\text{m/s}^2\) |
| 3. | \(32 \pi^2~\text{m/s}^2\) | 4. | \(16 \pi ~\text{m/s}^2\) |
Subtopic: Â Circular Motion |
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A car is moving on a circular path of radius \(600~\text{m}\) such that the magnitude of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete the first quarter of the revolution, if it is moving with an initial speed of \(54~\text{km/hr}\) is:
1. \(40[1-e^{-{\pi/2}}]~\text s\)
2. \(30[1-e^{-{\pi/2}}]~\text s\)
3. \(40[1+e^{-{\pi/2}}]~\text s\)
4. \(30[1+e^{-{\pi/2}}]~\text s\)
1. \(40[1-e^{-{\pi/2}}]~\text s\)
2. \(30[1-e^{-{\pi/2}}]~\text s\)
3. \(40[1+e^{-{\pi/2}}]~\text s\)
4. \(30[1+e^{-{\pi/2}}]~\text s\)
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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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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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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An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \({x}=+2~\text{m}, \) its velocity is \(-4\hat j~\text{m/s}. \) The object's velocity \((v)\) and acceleration \((a)~\) at \({x}=-2~\text{m} ~\) will be:
| 1. | \(v=-4 \hat{i}~\text{m/s}, ~~~{a}=-8 \hat{j}~\text{m/s}^2~\) |
| 2. | \(v=4 \hat{j} ~\text{m/s},~~~{a}=8 \hat{i} ~\text{m/s}^2 ~\) |
| 3. | \(v=-4 \hat{i} ~\text{m/s}, ~~~{a}=8 \hat{j} ~\text{m/s}^2~\) |
| 4. | \(v=4 \hat{i}~\text{m/s},~~~{a}=8 \hat{j} ~\text{m/s}^2 ~\) |
Subtopic: Â Circular Motion |
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