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.
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): In uniform circular motion of a particle, sum of power delivered to it by all the forces acting on the particle is zero.
Reason (R): In uniform circular motion dot product of two perpendicular vectors, force and velocity is always zero.
In UCM, net force is perpendicular to velocity, so power \(P = \vec{F} \cdot \vec{v} = Fv \cos{90^{\circ}}\) is zero. Thus, (A) is true. Reason (R) correctly states that the dot product of perpendicular vectors is zero, which explains (A).
Assertion (A): A body having uniform speed in circular path has a variable acceleration.
Reason (R): Direction of acceleration is always away from the centre.
In UCM, speed is constant but velocity direction changes, so acceleration exists (centripetal). Thus (A) is true. Acceleration is towards the center, not away. So (R) is false.
Assertion (A): In turning a vehicle safely with uniform speed in circular path friction is static in nature and towards centre.
Reason (R): In turning a vehicle in circular path with increasing speed friction is kinetic in nature and tangential in direction.
For safe turning at uniform speed, static friction provides the necessary centripetal force towards the center. So (A) is true. If speed increases, kinetic friction might act but it's not tangential; it opposes relative motion. So (R) is false.
Assertion (A): In uniform circular motion, magnitude of acceleration is \(\frac{V^2}{R}\) and direction is always towards the centre.
Reason (R): In uniform circular motion, acceleration is constant.
In UCM, centripetal acceleration is \(a = \frac{V^2}{R}\) towards the center. So (A) is true. Acceleration direction continuously changes, so it's not constant. So (R) is false.
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.
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): In non-uniform circular motion, linear speed of the body is variable.
Reason (R): In non-uniform circular motion, acceleration of the body is towards the centre.
In non-uniform circular motion, linear speed is variable, so (A) is true. The net acceleration has both radial (centripetal) and tangential components, so it's not solely towards the center. Thus, (R) is false.
Assertion (A): A body is moving along a circle with a variable angular speed. Work done by centripetal force will be zero.
Reason (R): In non-uniform circular motion, net force on the body is not in the radial direction.
Centripetal force is always perpendicular to displacement, so work done by it is zero. Thus, (A) is true. In non-uniform circular motion, a tangential force exists, so the net force is not purely radial. Thus, (R) is true. However, (R) does not explain (A).
Assertion (A): A body tied to an end of a string is whirled along a vertical circle by giving some velocity at the lowest position. If the velocity becomes zero before the tension in the string is zero, the body will leave the circular path at the position of its zero velocity and then fall vertically downward.
Reason (R): In vertical circular motion, tension in the string at the highest position is maximum.
If velocity becomes zero before tension, the object leaves the circular path and follows a parabolic trajectory, not vertically downward. So (A) is false.
Tension is maximum at the lowest point and minimum at the highest point in vertical circular motion. So (R) is false.
Assertion (A): A body tied to an end of a string is whirled along a vertical circle with such a velocity at the lowest point that, at some position, tension in the string is zero but the speed at the position is non-zero. The body will leave the circular path at the position of zero tension.
Reason (R): In vertical circular motion, so as to cross the highest point along the circle, speed at the highest point, \( v_H geq 0 \).
An object leaves a vertical circular path when tension becomes zero and speed is non-zero. So (A) is true. To complete a vertical circle, the minimum speed at the highest point is \( \sqrt{gR} \), not just \( 0 \). So (R) is false.