Assertion (A): A particle with constant acceleration always moves along a straight line.
Reason (R): A particle with constant acceleration will not change direction of motion.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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A projectile experiences constant acceleration (g) but follows a parabolic path. Also, a ball thrown vertically upwards under gravity has constant acceleration but reverses its direction of motion, making both statements false.
Assertion (A): A particle with constant acceleration always moves along a straight line.
Reason (R): A particle with constant acceleration will not change direction of motion.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false. Projectile motion has constant acceleration (\(\vec{g}\)) but follows a parabolic path, not a straight line.
Reason (R) is false. A particle can change direction even with constant acceleration (e.g., projectile motion, or an object slowing down and reversing direction).
Thus, both (A) and (R) are false.
Assertion (A): If initial velocity is negative and acceleration is positive then motion is retarded (initially).
Reason (R): If initial velocity is negative but acceleration is positive then displacement of a particle can never be positive.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is true because if velocity and acceleration have opposite signs (negative velocity, positive acceleration), the object is slowing down (retarding) initially.
Reason (R) is false. An object with negative initial velocity and positive acceleration can eventually reverse direction and achieve positive displacement (e.g., if it starts at \(x=0\), it will eventually cross \(x=0\) and move to positive \(x\)).
Thus, (A) is true, (R) is false.
Assertion (A): If initial velocity is negative but acceleration is positive then displacement of a particle can never be positive.
Reason (R): If initial velocity is negative and acceleration is positive then motion must be retarded throughout.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false. If initial velocity is negative and acceleration is positive, the particle can eventually move in the positive direction, leading to a positive displacement (e.g., \(s = v_0 t + \frac{1}{2}at^2\) can be positive for large \(t\)).
Reason (R) is false. Motion is initially retarded, but as velocity becomes positive (due to positive acceleration), the motion becomes accelerated.
Assertion (A): An object moving with a velocity of magnitude \(10 \text{ m/s}\) is subjected to a uniform acceleration \(2 \text{ m/s}^2\) at right angle to the initial motion. Its velocity after \(5s\) has a magnitude nearly \(14 \text{ m/s}\).
Reason (R): The equation \(\vec{v} = \vec{u} + \vec{a}t\) can be applied to obtain \(\vec{v}\) if \(\vec{a}\) is constant.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A): Given \(u = 10 \text{ m/s}\), \(a = 2 \text{ m/s}^2\), \(t = 5 \text{ s}\). Since \(\vec{u}\) and \(\vec{a}\) are perpendicular, the final velocity magnitude is \(|\vec{v}| = \sqrt{u^2 + (at)^2} = \sqrt{10^2 + (2 \times 5)^2} = \sqrt{100+100} = \sqrt{200} \approx 14.14 \text{ m/s}\). So (A) is true.
Reason (R): The equation \(\vec{v} = \vec{u} + \vec{a}t\) is valid when acceleration \(\vec{a}\) is constant. So (R) is true.
(R) correctly explains (A) as the formula is used due to constant acceleration.
Assertion (A): A coin is allowed to fall in a train moving with constant velocity. Its trajectory is a straight line as seen by observer attached to the train.
Reason (R): An observer on ground will see the path of coin as a parabola.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A): From the train's frame of reference (inertial, moving with constant velocity), the coin only has vertical motion under gravity, thus appearing as a straight line. So (A) is true.
Reason (R): From the ground frame, the coin has an initial horizontal velocity (that of the train) and vertical acceleration due to gravity, resulting in a parabolic path. So (R) is true.
However, (R) describes a different frame of reference and does not explain why the path is a straight line in the train's frame.