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Q. No.The following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general. Choose the incorrect statement(s):
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), (d)
2.
(a), (c)
3.
(b), (c)
4.
(a), (b)
Subtopic: Speed & Velocity |
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Given below are two statements:
| Assertion (A): | If two particles move with uniform accelerations in different directions, then their relative velocity changes in direction. |
| Reason (R): | Since the acceleration are in different directions, there is a relative acceleration and hence the relative velocity changes. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Relative Motion |
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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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Given below are two statements:
| Assertion (A): | When \(\theta=45\)° or \(135^\circ,\) the value of range, \(R\) remains the same, only the sign changes. |
| Reason (R): | \(R={u^2 sin \theta \over g}.\) |
| 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: Projectile Motion |
62%
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Given below are two statements:
| Assertion (A): | Linear momentum of a body changes even when it is moving uniformly in a circle. |
| Reason (R): | In uniform circular motion, velocity remains constant. |
| 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. | (A) is False but (R) is True. |
Subtopic: Circular Motion |
63%
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Given below are two statements:
| Assertion (A): | When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same time. |
| Reason (R): | Horizontal velocity has no effect on the vertical direction. |
| 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. | (A) is False but (R) is True. |
Subtopic: Projectile Motion |
78%
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Given below are two statements:
| Assertion (A): | Two similar trains are moving along the equator at the same speed but in opposite directions. They will exert equal pressure on the rails. |
| Reason (R): | In uniform circular motion, the magnitude of acceleration remains constant but the direction continuously changes. |
| 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. | (A) is false but (R) is true. |
Subtopic: Circular Motion |
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Given below are two statements:
| Assertion (A): | A projectile has only vertical component of velocity at the highest point of its trajectory. |
| Reason (R): | At the highest point, only one component of velocity is present. |
| 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. | (A) is False but (R) is True. |
Subtopic: Projectile Motion |
78%
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Select the correct option based on the statements given below:
| Assertion (A): | Generally, the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very large height. |
| Reason (R): | The path of a projectile is independent of the gravitational force of the earth. |
| 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: Projectile Motion |
61%
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Given below are two statements:
| Assertion (A): | A particle is projected at an angle \(\theta\) (<\(90^\circ\)) to horizontal, with a velocity \(u.\) When particle strikes the ground, its speed is again \(u.\) |
| Reason (R): | Velocity along horizontal direction remains the same but velocity along vertical direction is changed. When a particle strikes the ground, the magnitude of final vertical velocity is equal to the magnitude of the initial vertical velocity. |
| 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: Projectile Motion |
81%
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