Q. No.A force \((\hat{i}-3 \hat{j}+2 \hat{k})\) acts on a particle lying at origin. The torque acting on particle about the origin is:
1. Zero
2. \(3 \mathrm{~N}-\mathrm{m}\)
3. \(5 \mathrm{~N}-\mathrm{m}\)
4. \(2 \mathrm{~N}-\mathrm{m}\)
1. Zero
2. \(3 \mathrm{~N}-\mathrm{m}\)
3. \(5 \mathrm{~N}-\mathrm{m}\)
4. \(2 \mathrm{~N}-\mathrm{m}\)
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The moment of the force, at point (2, 0, -3) about the point (2, -2, -2) is given by:
1.
2.
3.
4.
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If the angular momentum of a body varies with time \(t\) as \(L=\left(5 t^3+6 t^2+9 t+1\right)~\text{kg m}^2/\text s.\) Then the torque acting on the body at \(t = 1~\text{s}\) is:
1. \(270~\text{N-m}\)
2. \(379~\text{N-m}\)
3. \(170~\text{N-m}\)
4. \(36~\text{N-m}\)
1. \(270~\text{N-m}\)
2. \(379~\text{N-m}\)
3. \(170~\text{N-m}\)
4. \(36~\text{N-m}\)
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If the ruler is in rotational equilibrium then the value of unknown weight is:
1. \(100 \mathrm{~N}\)
2. \(125 \mathrm{~N}\)
3. \(90 \mathrm{~N}\)
4. \(150 \mathrm{~N}\)
1. \(100 \mathrm{~N}\)
2. \(125 \mathrm{~N}\)
3. \(90 \mathrm{~N}\)
4. \(150 \mathrm{~N}\)
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A force \(\vec{{F}}=3 \hat{i}+4 \hat{j}-2 \hat{k}\) acts on a particle located at a position vector \(\vec{r}=2 \hat{i}+ \hat{j}+2 \hat{k}.\) What is the torque of this force about the origin?
1. \(3 \hat{i}+4 \hat{j}-2 \hat{k} \)
2. \(-10 \hat{i}+10 \hat{j}+5 \hat{k} \)
3. \(10 \hat{i}+5 \hat{j}-10 \hat{k} \)
4. \(10 \hat{i}+\hat{j}-5 \hat{k}\)
1. \(3 \hat{i}+4 \hat{j}-2 \hat{k} \)
2. \(-10 \hat{i}+10 \hat{j}+5 \hat{k} \)
3. \(10 \hat{i}+5 \hat{j}-10 \hat{k} \)
4. \(10 \hat{i}+\hat{j}-5 \hat{k}\)
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A wheel having a moment of inertia of \(2\) kg–m2 about its vertical axis rotates at the rate of \(60\) rpm about the axis. The torque which can stop the wheel's rotation in one minute would be:
| 1. | \(\dfrac{\pi }{12}\) N-m | 2. | \(\dfrac{\pi }{15}\) N-m |
| 3. | \(\dfrac{\pi }{18}\) N-m | 4. | \(\dfrac{2\pi }{15}\) N-m |
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AIPMT - 2004
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Choose the correct statement:
| 1. | Two equal and opposite forces whose line of action do not coincide make a couple. |
| 2. | For rotational equilibrium of a body, torque about its centre of mass is zero. |
| 3. | A body in translational equilibrium need not necessarily be in rotational equilibrium. |
| 4. | All of these |
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A body is rotating with an angular velocity of \(30~\text{rad/s}.\) An external torque of \(10~\text{N-m}\) is applied to the body in the same direction as its angular velocity. What is the instantaneous power delivered to the body?
| 1. | \(3000~\text{W}\) | 2. | \(300~\text{W}\) |
| 3. | \(1500~\text{W}\) | 4. | \(150~\text{W}\) |
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A disc is rotating with angular velocity \(\vec{\omega} .\) A force \(\vec{F}\)acts at a point whose position w.r.t axis of rotation is \(\vec{r}\). The torque due to force is given by:
1. \((\vec{r} \times \vec{F})\)
2. \((\vec{F} \times \vec{r})\)
3. \(\vec{F} \cdot \vec{r}\)
4. \(\vec{r} \cdot(\vec{F} \cdot \vec{\omega})\)
1. \((\vec{r} \times \vec{F})\)
2. \((\vec{F} \times \vec{r})\)
3. \(\vec{F} \cdot \vec{r}\)
4. \(\vec{r} \cdot(\vec{F} \cdot \vec{\omega})\)
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A flywheel with a moment of inertia of \(2~\text{kg-m}^2\) is initially rotating at an angular speed of \(30~\text{rad/s}.\) A tangential force applied at the rim brings the flywheel to a stop in \(15 \text{ s}\). The average torque exerted by the force is:
1. \(4~\text{N-m}\)
2. \(2~\text{N-m}\)
3. \(8~\text{N-m}\)
4. \(1~\text{N-m}\)
1. \(4~\text{N-m}\)
2. \(2~\text{N-m}\)
3. \(8~\text{N-m}\)
4. \(1~\text{N-m}\)
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