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Q. No.The displacement of the point \(P\) on the wheel (see figure) as the wheel completes half revolution while rolling on the ground is:
1. \(2\pi r\)
2. \(\pi r\)
3. \(\pi r+2r\)
4. \(r\sqrt{\pi^2+4}\)
Subtopic: Position & Displacement |
73%
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Two inclined planes are placed as shown in the figure. A block is projected from the Point \(A\) of the inclined plane \(AB\) along its surface with a velocity just sufficient to carry it to the top point \(B\) at a height of \(10~\text m.\) After reaching the point \(B\) the block slides down on the inclined plane \(BC.\) The time it takes to reach the point \(C\) from the point \(A\) is \(t( \sqrt 2 + 1 )~\text{s}.\) The value of \(t\) is:
(Take \(g=10~\text{m/s}^2\) )
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
(Take \(g=10~\text{m/s}^2\) )
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Uniformly Accelerated Motion |
61%
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JEE
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A person moves from point \(A\) to point \(B\) along a circular path, as shown in the figure below. If the distance traveled by the person is \(60\) m, then the magnitude of displacement would be: (given that \(\cos135^\circ =-0.7\))
| 1. | \(42\) m | 2. | \(47\) m |
| 3. | \(19\) m | 4. | \(40\) m |
Subtopic: Position & Displacement |
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JEE
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Given below are two statements:
| 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 True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Circular Motion |
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Given below are two statements:
| 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. |
Subtopic: Speed & Velocity |
54%
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Given below are two statements:
| 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. |
Subtopic: Projectile Motion |
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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. \(0^\circ\)
Subtopic: Circular Motion |
66%
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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
Subtopic: Speed & Velocity |
63%
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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
Subtopic: Uniformly Accelerated Motion |
71%
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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
Subtopic: Uniformly Accelerated Motion |
64%
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