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Question: A bird dismounts on the stretched telegraph wire. The additional tension produced in the wire is: ...

A bird dismounts on the stretched telegraph wire. The additional tension produced in the wire is:
(A) Zero
(B) Greater than the weight of the bird
(C) Less than the weight of the bird
(D) Equal to the weight of the bird

Explanation

Solution

In this question, it is given that when the bird settles itself on the wire it gets stretched as a result tension is produced in the wire. Tension is a force of pulling that is axially transmitted along the wire. Therefore the solution can be evaluated by comparing the weight of the bird with the tension produced in the wire when the bird dismounts itself on the wire.

Complete answer:
Assume that the tension on the wire would be equal to TT as it is stretched before the bird sits on it. Now when the bird sits on the wire then it is stretched a little more as the weight of the bird is very small.

From the figure, it can be evaluated as that when the bird sat on the wire it got stretched and tension is produced in the wire which is being balanced by the weight of the bird. As the Tension T′T'is being new tension on the wire when the bird sat on it. Now the component of the tension would be equal to 2T′sin⁡θ2T'\sin \theta which is balanced by the weight of the bird WW
⇒W=2T′sin⁡θ\Rightarrow W = 2T'\sin \theta -------- Equation (1)(1)
Where,mmis the mass of the bird, and ggis the gravitational acceleration.
Substituting the value of weight WWin the equation (1)(1)
⇒mg=2T′sin⁡θ\Rightarrow mg = 2T'\sin \theta
Rearranging the equation
⇒T′=mg2sin⁡θ\Rightarrow T' = \dfrac{{mg}}{{2\sin \theta }}
As the angle is very small which can be observed from the figure. Hence it sin⁡θ\sin \theta can be considered very small. Therefore it results in larger tension in the wire
Therefore the tension T′T' is greater than the weight WW of the wire.

Hence option (B) is the correct answer.

Note:
Here the Tension mentioned above is a type of force and in physics, the word tension means to stretch. It is useful to find how much force is acting on the substance like extension cable, strings, etc. when they are stretched or pulled. Its unit is Newton(N) as it is a type of force.