Assertion (A) is true: When a bird sits on a wire, causing it to sag slightly, the vertical components of tension in the two halves of the wire balance the bird's weight. Since the sag is slight, the angle the wire makes with the horizontal is small. To have vertical components sum up to the bird's weight \(W\), the tension \(T\) in each part of the wire must be much larger than \(W/2\) (specifically, if \(theta\) is the angle, \(2Tsin(theta) = W\)). Given \(sin(theta)\) is small, \(T\) must be large, often significantly more than \(W\).nReason (R) is true: As explained, for the small vertical components of tension to balance the bird's weight, the overall tension in the wire must be considerably larger than the weight itself. Reason (R) correctly explains why this phenomenon occurs. Therefore, (A) and (R) are true, and (R) is the correct explanation of (A).

Assertion (A) is false: When two particles interact, they exert forces on each other. Unless these interaction forces are exactly balanced by other external forces, the net force on *either* particle will generally *not* be zero, causing them to accelerate. Only the net force on the *system* of two interacting particles is zero (if no external forces are present).

Reason (R) is true: According to Newton's third law, when two particles interact, they exert action and reaction forces on each other which are always equal in magnitude and opposite in direction. Given that (A) is false and (R) is true, and option 'A is false but R is true' is not explicitly provided, option (4)

'Both (A) and (R) are false' is selected as it correctly identifies (A) as false.

Assertion (A) is true: Since both blocks are on smooth surfaces (implying no friction between blocks), a force applied *only* to the upper block will not be transmitted horizontally to the lower block. The upper block will slide over the lower. The lower block will continue to accelerate down the smooth inclined plane solely due to gravity.

Reason (R) is true: The acceleration of any block on a smooth inclined plane (where \(theta\) is the angle of inclination) is indeed \(g sin(theta)\), assuming no other forces. Reason (R) states a fact about acceleration on an inclined plane. While it describes the acceleration of the lower block, it does not explain *why* the force on the upper block has no effect on it (which is due to the lack of friction between them).

Therefore, (A) and (R) are true, but (R) is not the correct explanation of (A).

Assertion (A) is true: Newton's third law states that action and reaction forces are always equal in \(magnitude\) and opposite in \(direction\).nReason (R) is false: Action and reaction forces act on *different* bodies, so they cannot cancel each other out to produce a net force of \(0\) on a *single* body. Therefore, (A) is true but (R) is false.

Assertion (A) is true: When an elevator accelerates upwards with acceleration \(a\), the pseudo force on an object inside is \(ma\) downwards (in the non-inertial frame). So, for upward accelerating elevator, pseudo force on a block is downward.nReason (R) is false: Pseudo force is not a real force applied by the lift; it is an inertial force experienced in a non-inertial reference frame, acting opposite to the acceleration of the frame, not necessarily the direction of motion. Therefore, (A) is true but (R) is false.

Assertion (A) is true: the man exerts a force equal to his weight on the ground. Reason (R) is true by Newton's third law of gravitation for action-reaction. However, Reason (R) explains gravitational forces, not the contact force on the ground, so it is not a correct explanation for (A).

Assertion (A) is false; zero acceleration implies zero \(\text{net}\) force, not zero individual forces. Reason (R) is false; a single force causes \(text{acceleration}\) in its direction, not necessarily motion in that direction if initial velocity is present.

Assertion (A) is true due to low friction on ice. Reason (R) is also true as small steps are needed to minimize horizontal forces and prevent slipping. (R) explains why extra effort and carefulness are required, making the activity tiring.

Assertion (A) is true. Earth is a non-inertial frame, so frames observing a particle on Earth can also be non-inertial. Reason (R) is false because a frame attached to Earth is technically non-inertial due to Earth's rotation and orbital motion.

Assertion (A) is true: contact force is the resultant of normal and friction forces from the surface. Reason (R) is true: for a body at rest on a horizontal surface, contact force magnitude is equal to \(mg\). (R) is a specific case, not a general explanation of (A)'s definition.