Q. No.Which of the following is the angle between velocity and acceleration of a body in uniform circular motion?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)
| 1. | \(\dfrac{{v}^{2}}{r}\) | 2. | \(a\) |
| 3. | \(\sqrt{{a}^{2}{+}{\left({\dfrac{{v}^{2}}{r}}\right)}^{2}}\) | 4. | \(\sqrt{a+\dfrac{v^{2}}{r}}\) |
| 1. | \(2:\sqrt3\) | 2. | \(\sqrt3:2 \) |
| 3. | \(\sqrt3:1\) | 4. | \(1:\sqrt{3}\) |
The angle turned by a body undergoing circular motion depends on time as \(\theta=\theta_0+\theta_1t+\theta_2t^2.\) Then the angular acceleration of the body is
1. \(\theta_1\)
2. \(\theta_2\)
3. \(2\theta_1\)
4. \(2\theta_2\)
A particle moves in a circle of radius \(5\text{ cm}\) with constant speed and time period \(0.2\pi \text{ sec}.\) The acceleration of the particle is:
1. \(25\text{ m/s}^2\)
2. \(36\text{ m/s}^2\)
3. \(5\text{ m/s}^2\)
4. \(15\text{ m/s}^2\)
| 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. | \(\vec{v}_A=3 \hat{i}~\text{m/s} ;~\vec{a}_A=9 \hat{j}~\text{m/s}^2 \) |
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. \(16 \pi ~\text{m/s}^2\)
1. \(\sqrt{20}~\text{cm/s}^2\)
2. \(\sqrt{10}~\text{cm/s}^2\)
3. \(20~\text{cm/s}^2\)
4. \(10~\text{cm/s}^2\)
1. \(4m\pi \nu^2R \)
2. \(4\pi^2 \nu R \)
3. \(4\pi^2 \nu^2R \)
4. \(4\pi^2 \nu^2R^2 \)
1. \(\overrightarrow{a}_1\)
2. \(\overrightarrow{a}_2\)
3. \(\overrightarrow{a}_3\)
4. none of the above
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