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)
The figure shows a lamina in XY-plane. Two axes 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 P is closer to the z'-axis than the z-axis.)
(a) | torque \(\vec{\tau}\) caused by \(\vec{F}\) about 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 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)
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) | \(a/3\) from A, no motion. | normal reaction effectively at
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) |