# 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) vav = 1/2 [v(t1) + v(t2)] (b) vav = r(t2)-r(t1)/t2-t1 (c) r = 1/2 [v(t2)-v(t1)](t2-t1) (d) aav = v(t2)-v(t1)/t2-t1 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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Select the correct option based on the statements given below:

 Assertion: The maximum height of a projectile is always $$25$$% of the maximum range. Reason: For maximum height, the projectile should be projected at $$90^\circ.$$

 1 Both assertion and reason are correct, reason is the correct explanation of Assertion. 2 Both assertion and reason are correct but the reason is not the correct explanation of the assertion. 3 Assertion is correct and the reason is incorrect. 4 Assertion is incorrect and the reason is correct.
Subtopic:  Projectile Motion |
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Assertion: When $$\theta=45$$° or 135°, the value of  R remains the same, only the sign changes.
Reason: $$R={u^2 sin \theta \over g}$$
1. Both assertion and reason are true and the reason is the correct explanation of the assertion.
2. Both assertion and reason are true but the reason is not the correct explanation of the assertion.
3. Assertion is true but the reason is false.
4. Both assertion and reason are false.

Subtopic:  Projectile Motion |
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Select the correct option based on statements below:
 Assertion: Linear momentum of a body changes even when it is moving uniformly in a circle. Reason: In uniform circular motion, velocity remains constant.

 1 Both assertion and reason are true and the reason is the correct explanation of the assertion. 2 Both assertion and reason are true but the reason is not the correct explanation of the assertion. 3 Assertion is true but the reason is false. 4 Both assertion and reason are false.
Subtopic:  Circular Motion |
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Assertion: When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same time.
Reason: Horizontal velocity has no effect on the vertical direction.
1. Both the assertion and reason are true and reason explains the assertion.
2. Both the assertion and reason are true but reason does not explain the assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.
Subtopic:  Projectile Motion |
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Assertion: Two similar trains are moving along the equator at the same speed but in opposite direction. They will exert equal pressure on the rails.
Reason: In uniform circular motion the magnitude of acceleration remains constant but the direction continuously changes.
1. Both the assertion and reason are true and reason explains the assertion.
2. Both the assertion and reason are true but reason does not explain the assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.

Subtopic:  Circular Motion |
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Assertion: A projectile has only vertical component of velocity at the highest point of its trajectory.
Reason: At the highest point, only one component of velocity is present.
1. Both the assertion and reason are true and reason explains the assertion.
2. Both the assertion and reason are true but reason does not explain the assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.

Subtopic:  Projectile Motion |
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Assertion: Generally, the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very large height.
Reason: The path of a projectile is independent of the gravitational force of the earth.
1. Both assertion & reason are true and the reason is the correct explanation of the assertion
2. Both assertion & reason are true but the reason is not the correct explanation of the assertion
3. Assertion is true but reason is false.
4. Both assertion and reason are false statements.

Subtopic:  Projectile Motion |
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Assertion: A particle is projected at an angle $$\theta$$ (<90°) to horizontal, with a velocity u. When particle strikes the ground, its speed is again u.
Reason: 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 assertion & reason are true and the reason is the correct explanation of the assertion
2. Both assertion & reason are true but the reason is not the correct explanation of the assertion
3. Assertion is true but reason is false.
4. Both assertion and reason are false statements.

Subtopic:  Projectile Motion |
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