Assertion (A): A bird sits on a stretched wire depressing it slightly. The increase in tension of the wire is more than the weight of the bird.
Reason (R): The tension must be more than the weight as it is required to balance weight.
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).