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. \(3 \text{ N-m}\)
3. \(5 \text{ N-m}\)
4. \(2 \text{ N-m}\)
1. Zero
2. \(3 \text{ N-m}\)
3. \(5 \text{ N-m}\)
4. \(2 \text{ N-m}\)
Subtopic: Â Torque |
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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. \(36~\text{N-m}\)
Subtopic: Â Torque |
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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. \(150 \mathrm{~N}\)
Subtopic: Â Torque |
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Choose the correct statement:
| 1. | Two equal and opposite forces whose lines 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. |
Subtopic: Â Torque |
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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. | \(150~\text{W}\) |
Subtopic: Â Torque |
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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. \(\vec{r} \cdot(\vec{F} \cdot \vec{\omega})\)
Subtopic: Â Torque |
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An automobile engine delivers \(100~ \text{kW}\) of power while running at an angular speed of \(250~\text{rad/s}.\) The torque produced by the engine is:
1. \(680 ~\text {N-m}\)
2. \(480 ~\text {N-m}\)
3. \(580 ~\text {N-m}\)
4. \(400 ~\text {N-m}\)
1. \(680 ~\text {N-m}\)
2. \(480 ~\text {N-m}\)
3. \(580 ~\text {N-m}\)
4. \(400 ~\text {N-m}\)
Subtopic: Â Torque |
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The torque of a force \(5 \hat i + 3 \hat j - 7 \hat k\) about the origin is \(\tau\). If the force acts on a particle whose position vector is \(2 \hat i + 2 \hat j + \hat k\), then the value of \(\tau\) will be:
1. \(11 \hat{i}+19 \hat{j}-4 \hat{k} \)
2. \(-11 \hat{i}+9 \hat{j}-16 \hat{k} \)
3. \(-17 \hat{\mathrm{i}}+19 \hat{\mathrm{j}}-4 \hat{\mathrm{k}} \)
4. \(17 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+16 \hat{\mathrm{k}}\)
1. \(11 \hat{i}+19 \hat{j}-4 \hat{k} \)
2. \(-11 \hat{i}+9 \hat{j}-16 \hat{k} \)
3. \(-17 \hat{\mathrm{i}}+19 \hat{\mathrm{j}}-4 \hat{\mathrm{k}} \)
4. \(17 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+16 \hat{\mathrm{k}}\)
Subtopic: Â Torque |
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Many of the trails seen at Yosemite National Park in America were constructed by the Civil Conservation Corps, an organization established under President Roosevelt's administration. One of the ways that they were able to move chunks of large granite was to make use of a fulcrum. Suppose a \(2.5~\text{m}\) steel bar is placed under a rock weighing \(3000~\text{N}\). A fulcrum is set \(0.5~\text{m}\) away from the rock to be moved. What force must be exerted on the other end of the bar to move the rock?
(neglect the mass of the bar)
1. \(600~\text{N}\)
2. \(750~\text{N}\)
3. \(3000~\text{N}\)
4. \(12000~\text{N}\)
(neglect the mass of the bar)
1. \(600~\text{N}\)
2. \(750~\text{N}\)
3. \(3000~\text{N}\)
4. \(12000~\text{N}\)
Subtopic: Â Torque |
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A brother and sister fight over whether a door should be opened or closed. They both push with the same magnitude of force, perpendicular to the door, as shown in the figure. Which sibling exerts more torque on the door, with respect to the hinge?
| 1. | The sister. |
| 2. | The brother. |
| 3. | They both exert the same torque. |
| 4. | It depends upon the length of the door. |
Subtopic: Â Torque |
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