Q. No.What would be the torque about the origin when a force \(3\hat{j}~\text N\) acts on a particle whose position vector is \(2\hat{k}~\text m?\)
| 1. | \(6\hat{j}~\text{N-m}\) | 2. | \(-6\hat{i}~\text{N-m}\) |
| 3. | \(6\hat{k}~\text{N-m}\) | 4. | \(6\hat{i}~\text{N-m}\) |
A meter scale is moving with uniform velocity. This implies:
| 1. | the force acting on the scale is zero, but a torque about the centre of mass can act on the scale. |
| 2. | the force acting on the scale is zero and the torque acting about the centre of mass of the scale is also zero. |
| 3. | the total force acting on it need not zero but the torque on it is zero. |
| 4. | neither the force nor the torque needs to be zero. |
Let \(\vec{F}\) be a force acting on a particle having position vector \(\vec{r}\). Let \(\vec{\tau}\) be the torque of this force about the origin, then:
| 1. | \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\) |
| 2. | \(\vec{r} \cdot \vec{\tau}=0\) but \(\vec{F} \cdot \vec{\tau} \neq 0\) |
| 3. | \(\vec{r} \cdot \vec{\tau} \neq 0\) but \(\vec{F} \cdot \vec{\tau}=0\) |
| 4. | \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\) |
| 1. | \({\dfrac b 2}\) | 2. | \({ \dfrac b 4}\) |
| 3. | \({\dfrac b 8}\) | 4. | \(\dfrac b 3\) |
Two forces \(F\) of equal magnitude act on a beam. Which diagram shows a couple of actions and states the magnitude of the torque (moment) of the couple about the pivot?
(The pivot is at the center of the beam.)
| 1. |  |
| 2. |  |
| 3. |  |
| 4. |  |
If the force \(7\hat i+3\hat j-5\hat k\) acts on a particle whose position vector is \(\hat i - \hat j+\hat k\), the torque of the force about the origin is?
1. \(2\hat i +12\hat j+10\hat k\)
2. zero
3. \(2\hat i -12\hat j-10\hat k\)
4. \(2\hat i +12\hat j-10\hat k\)
The figure shows a lamina in \(\text{XY}\)-plane. Two axes \(\text{z}\) and \(z'\) pass perpendicular to its plane. A force \(\vec{F}\) acts in the plane of the lamina at point P as shown. (The point \(\text{p}\) is closer to the \(z'\)-axis than the \(\text{z}\)-axis.)
| (a) | torque \(\vec{\tau}\) caused by \(\vec{F}\) about \(\text{z}\)-axis is along - \(\hat{k}\) |
| (b) | torque \(\vec{\tau}'\) caused by \(\vec{F}\) about \(z'\)-axis is along - \(\hat{k}\) |
| (c) | torque caused by \(\vec{F}\) about the \(\text{z}\)-axis is greater in magnitude than that about the z'-axis |
| (d) | total torque is given by \(\vec{\tau}_{net}=\vec{\tau}+\vec{\tau}'\) |
Choose the correct option:
1. (c, d)
2. (a, c)
3. (b, c)
4. (a, b)
The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
| (a) | The forces may be acting radially from a point on the axis. |
| (b) | The forces may be acting on the axis of rotation. |
| (c) | The forces may be acting parallel to the axis of rotation. |
| (d) | The torque caused by some forces may be equal and opposite to that caused by other forces. |
Choose the correct option.
1. (a, c, d)
2. (a, b, d)
3. (a, b, c, d)
4. (b, c, d)
A uniform cube of mass \(m\) and side \(a\) is placed on a frictionless horizontal surface. A vertical force \(F\) is applied to the edge as shown in the figure. Match the following (most appropriate choice).
| List- I | List- II | ||
| (a) | \(mg/4<F<mg/2\) | (i) | cube will move up. |
| (b) | \(F>mg/2\) | (ii) | cube will not exhibit motion. |
| (c) | \(F>mg\) | (iii) | cube will begin to rotate and slip at \(A\). |
| (d) | \(F=mg/4\) | (iv) | normal reaction effectively at \(a/3\) from \(A\), no motion. |
| 1. | a - (i), b - (iv), c - (ii), d - (iii) |
| 2. | a - (ii), b - (iii), c - (i), d - (iv) |
| 3. | a - (iii), b - (i), c - (ii), d - (iv) |
| 4. | a - (i), b - (ii), c - (iv), d - (iii) |
A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium?
(Take \(g=10~( \text {m/s}^2)\)
| 1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
| 3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
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