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A bird of weight W is resting at the center of a stretched wire of negligible mass. Each half of the wire makes a small angle with the horizontal. What can be concluded about the tension T in the wire? (A) T (B) W/2 ≤ T ≤ W (C) T > W (D) More information is needed to answer the question.

A bird of weight W is resting at the center of a stretched wire of negligible mass. Each half of the wire makes a small angle with the horizontal. What can be concluded about the tension T in the wire?  (A) T
(B) W/2 ≤ T ≤ W                          
(C) T > W
(D) More information is needed to answer the question.

Grade:upto college level

2 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
The correct option is:233-246_9.PNG
The figure below shows the free body diagram of the bird-string system, the forces acting on the bird and the stretched string. Assume that W represents the magnitude of weight of the bird, θrepresents the angle of the rope with horizontal whereas T represents the magnitude of tension in the string.
233-516_10.PNG
If there is no horizontal or vertical motion of the bird and string, the forces along in the horizontal direction and in the vertical direction must individually sum to zero.

That is,
T cos θ = T cos θ
2T sin θ = W
From the second equat6ion, we have
2T sin θ = W
T = \frac{W/2}{sin \theta }
For, values of sin θ lying between 0 and 1, the tension in the rope will always be greater than W/2, but it can never exceed W.
Therefore (b) is the correct option while the others are ruled out.
Dinesh Mehta
11 Points
3 years ago
Why tension can't exceed W . When sin theta is less than half than T will be greater than W .  And for small angles sin will be less so value may be more than W 

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