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): In a two-dimensional motion, there are two accelerations acting on the particle. Reason (R): Both the components of velocity, i.e., horizontal and vertical, in case of free fall keep on changing with respect to time.

 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:  Acceleration |
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Given below are two statements:
 Assertion (A): Path of the particle thrown with some velocity at some angle $$\theta$$ (not $$90^\circ$$ with the horizontal) is a parabola. Reason (R): If the angle between acceleration and velocity is $$0^\circ$$ and $$180^\circ,$$ the trajectory of the particle is a straight line.

 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 |
67%
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Given below are two statements:
 Assertion (A): If two particles are moving on the same circle in the same direction with different uniform angular speeds $$\omega_A \text{and } \omega_B$$, then the angular velocity of B relative to A for an observer at the centre will be $$\omega_B-\omega_A$$. Reason (R): In a uniform circular motion the body is constantly in equilibrium.

 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): If in a projectile motion, we take air friction into consideration, then tascent

 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 |
66%
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Given below are two statements:
 Assertion (A): The maximum horizontal range of projectile is proportional to the square of velocity. Reason (R): The maximum horizontal range of projectile is equal to maximum height attained by projectile.

 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 |
83%
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Given below are two statements:
 Assertion (A): When a particle moves in a circle with a uniform speed, both its velocity and acceleration change. Reason (R): The centripetal acceleration in circular motion is independent of the angular velocity of the body.

 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:  Uniformly Accelerated Motion |
60%
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Given below are two statements:
 Assertion (A): For angular projection, when angle of projection $$\theta = tan^{-1}(1),$$ the horizontal range is four times of the maximum height. Reason (R): The horizontal range of projectile is directly proportional to the square of velocity and inversely proportional to acceleration due to gravity.

 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 |
77%
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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:  Position & Displacement |
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Given below are two statements:
 Assertion (A): The relative velocity between any two bodies may be equal to the sum of the speeds of the two bodies. Reason (R): Sometimes, the relative velocity between two bodies may be equal to the difference in the speeds of the two.

 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:  Relative Motion |
76%
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