Assertion (A): Path of a projected ball is parabolic in uniform gravitational field for oblique projection in absence of air resistance.
Reason (R): Gravitational force is always act perpendicular to velocity during the motion of a projectile.
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
View Answer
The path of a projectile is a parabola under constant gravitational acceleration. Gravitational force acts vertically downwards, which is perpendicular to the velocity only at the highest point of its trajectory, so R is false.
Assertion (A): In any interval, the magnitude of displacement is always less than or equal to the distance travelled.
Reason (R): For a particle travelling in a straight line with constant acceleration, the magnitude of the change in the velocity during any interval is always less than or equal to the change in the speed during that interval.
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
View Answer
Displacement is the straight-line distance, so its magnitude is always \(le\) distance. When a particle reverses its direction of motion, the magnitude of change in velocity can be greater than the change in speed, so R is 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. 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
View Answer
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): Path of a projected ball is parabolic in uniform gravitational field for oblique projection in absence of air resistance.
Reason (R): Gravitational force is always act perpendicular to velocity during the motion of a projectile.
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 true because projectile motion under gravity without air resistance follows a parabolic path.
Reason (R) is false as gravitational force acts perpendicular to velocity only at the peak of the trajectory, not always. Thus, (A) is true, (R) is false.
Assertion (A): In any interval, the magnitude of displacement is always less than or equal to the distance travelled.
Reason (R): For a particle travelling in a straight line with constant acceleration, the magnitude of the change in the velocity during any interval is always less than or equal to the change in the speed during that interval.
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 true because displacement is the shortest path, so its magnitude is always less than or equal to the distance travelled. Reason (R) is false. For example, if velocity changes from \(-5 \text{ m/s}\) to \(+5 \text{ m/s}\), change in velocity magnitude is \(10 \text{ m/s}\), but change in speed is \(0 \text{ m/s}\). Thus, (A) is true, (R) is 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
View Answer
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): When a particle is observed from two different inertial reference frames the general shape of the trajectory of particle is same.
Reason (R): The position vector of a particle and its velocity are frame independent quantities.
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
The general shape of a particle's trajectory is invariant across inertial reference frames. However, position vectors and velocities are frame-dependent quantities, changing with the relative motion of frames. Therefore, assertion (A) is true, but reason (R) is false.
Assertion (A): The speedometer of an automobile measures the average speed of the automobile.
Reason (R): Average velocity is equal to total distance divided by total time taken.
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
A speedometer measures instantaneous speed, not average speed. Average velocity is defined as total displacement divided by total time, while average speed is total distance divided by total time. Both assertion (A) and reason (R) are incorrect.
Assertion (A): Two bodies of masses \(M\) and \(m\) (\(M > m\)) are allowed to fall from the same height if the air resistance force for each be the same then both the bodies will reach the earth simultaneously.
Reason (R): For same air resistance, acceleration of both the bodies will be same.
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
If the air resistance force \(F_{/text{air}}\) is the same for both bodies, the net force is \(mg - F_{/text{air}}\). The acceleration is \(a = g - F_{/text{air}}/m\). Since masses \(M\) and \(m\) are different, their accelerations will be different. Thus, they will not reach the earth simultaneously, and their accelerations will not be the same. Both assertion and reason are false.