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Q. No.Given below are two statements:
| Assertion (A): | When a body is projected at an angle of \(45^\circ,\) its range is maximum. |
| Reason (R): | For maximum range, the value of \(\text{sin}2 \theta\) should be equal to one. |
| 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 |
88%
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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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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) | \(a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}\) |
Choose the incorrect option from the given ones:
1. (a) and (d) only
2. (a) and (c) only
3. (b) and (c) only
4. (a) and (b) only
Subtopic: Speed & Velocity |
64%
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For a particle performing uniform circular motion,
| (a) | the magnitude of particle velocity (speed) remains constant. |
| (b) | particle velocity is always perpendicular to the radius vector. |
| (c) | the direction of acceleration keeps changing as the particle moves. |
| (d) | angular momentum is constant in magnitude but direction keeps changing. |
Choose the correct statement/s:
| 1. | (c), (d) | 2. | (a), (c) |
| 3. | (b), (c) | 4. | (a), (b), (c) |
Subtopic: Circular Motion |
75%
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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 |
63%
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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 |
64%
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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 |
79%
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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 |
79%
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