Assertion (A): Whenever a particle moves in a circular path with uniform speed, an acceleration exists which is directed towards the centre
Reason (R): The net acceleration of a particle in circular motion is always radially inward.
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
In UCM, there is always centripetal acceleration towards the center, even if speed is uniform, due to change in velocity direction. So (A) is true. In UCM, the only acceleration is centripetal, which is radially inward. So (R) is true and explains (A).
Assertion (A): If the speed of a body is constant, the body cannot have a path other than a circular or straight line path.
Reason (R): It is not possible for a body to have a constant speed in an accelerated 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
A body can have constant speed and follow a curvilinear path (e.g., parabolic trajectory if air resistance is ignored). So (A) is false. A body can have constant speed but changing direction, leading to acceleration (e.g., UCM). So (R) is false.
Assertion (A): In circular motion, centripetal and centrifugal forces act in opposite directions and balance each other.
Reason (R): Centripetal force is a pseudo force.
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
Centripetal force is a real force causing circular motion. Centrifugal force is a pseudo force in a non-inertial frame. They are not interaction pairs and do not balance each other. So (A) is false. Centripetal force is a real force. So (R) is false.
Assertion (A): In uniform circular motion of a body, its linear speed remains constant.
Reason (R): In uniform circular motion total acceleration of the body has no radial component.
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
By definition, uniform circular motion means constant linear speed. So (A) is true. In UCM, the only acceleration is centripetal, which is entirely radial and directed towards the center. So (R) is false.
Assertion (A): Two identical trains move in opposite sense in equatorial plane with equal speed relative to earth’s surface. They have equal magnitude of normal reaction.
Reason (R): The trains require same centripetal force although they have different speeds.
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 absolute speed of the trains relative to Earth's center is \( v_{\text{abs}} = R_E \omega_E pm v_{\text{surface}} \). Since their absolute speeds are different, the centripetal force required \( F_c = m v_{\text{abs}}^2 / R_E \) will be different. The normal reaction is \( N = mg - F_c \), so it will also be different. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): A coin is placed on the gramophone. When the motor starts, the coin moves along the gramophone. As the speed goes on increasing, the coin flies off after some time.
Reason (R): The gravitational force of gramophone provides the necessary centripetal force to the coin.
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
Assertion (A) is true: As the angular speed \( \omega \) of the gramophone increases, the required centripetal force \( m \omega^2 r \) for the coin increases. When this force exceeds the maximum static friction (\( \mu_s mg \)), the coin slips off.
Reason (R) is false: The centripetal force is provided by the frictional force between the coin and the gramophone, not by the gravitational force. Gravitational force provides the normal force.