# 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 |
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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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