Q. No.The magnitude of vector \(\vec{A}\) is constant but it is changing its direction continuously. The angle between \(\vec {A}\) and \(\frac{d \vec{A}}{dt}\) is:
1. \(180^\circ\)
2. \(120^\circ\)
3. \(90^\circ\)
4. \(0^\circ\)
1. \(180^\circ\)
2. \(120^\circ\)
3. \(90^\circ\)
4. \(0^\circ\)
The following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general.
| (a) | \(v_{avg}=\frac{1}{2} [ v(t_{1})+v(t_{2}) ]\) |
| (b) | \(v_{avg}=\frac{r(t_{2})-r(t_{1})}{t_{2}-t_{1}}\) |
| (c) | \(r=\frac{1}{2}[ v(t_{2})-v(t_{1}) ](t_2-t_1)\) |
| (d) | \(a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}\) |
1. (a) and (d) only
2. (a) and (c) only
3. (b) and (c) only
4. (a) and (b) only
| Assertion (A): | The maximum height of a projectile is always \(25\)% of the maximum range. |
| Reason (R): | For maximum height, the projectile should be projected at \(90^\circ.\) |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True and (R) is False. |
| 4. | (A) is False and (R) is True. |
| Assertion (A): | For a given initial and final position the average velocity is single-valued while the average speed can have many values. |
| Reason (R): | Velocity is a vector quantity and speed is a scalar quantity. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
| Assertion (A): | Uniform circular motion is the only example of a situation in which the speed of a particle remains constant even though a force is acting on the particle. |
| Reason (R): | In uniform circular motion, a force acting along the circle pushes the particle forward. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is False but (R) is True. |
| 4. | Both (A) and (R) are False. |
| 1. | \(42\) m | 2. | \(47\) m |
| 3. | \(19\) m | 4. | \(40\) m |
(take \(g=10~\text{m/s}^2\))
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(2\pi r\)
2. \(\pi r\)
3. \(\pi r+2r\)
4. \(r\sqrt{\pi^2+4}\)
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2.\) What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84~\text m?\)
1. \(36~\text{m/s}\)
2. \(26~\text{m/s}\)
3. \(1~\text{m/s}\)
4. Zero
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \({x\text -y}\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0 \hat j)~\text{m/s}^2.\) What is the \({y\text -}\)coordinate of the particle at the instant its \({x\text -}\)coordinate is \(84~\text m?\)
1. \(36~\text m\)
2. \(26~\text m\)
3. \(1~\text m\)
4. Zero
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