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Chapter 10: Problem 81

A wire fixed at the upper end stretches by length \(l\) by applying a force \(F .\) The work done in stretching is [2004] (A) \(F / 2 l\) (B) \(F l\) (C) \(2 F l\) (D) \(F l / 2\)

Short Answer

Expert verified
The work done in stretching the wire is given by the formula \(W = F \cdot d\), where \(F\) is the force applied and \(d\) is the distance moved in the direction of the force. In this case, the distance is the length \(l\) by which the wire stretches. So, the work done is \(W = F \cdot l\), which corresponds to option (B).

Step by step solution

01

Recall the formula for work done

Work done is the product of force and the distance moved in the direction of the force. The formula for work done is given by: $$ W = F \cdot d \cdot \cos\theta $$ where \(W\) is the work done, \(F\) is the force applied, \(d\) is the distance moved in the direction of the force, and \(\theta\) is the angle between the force and the direction of motion. In this case, given that the force is applied in the direction of stretching, the angle between the force and the direction of motion is \(0^{\circ}\), so \(\cos\theta = \cos(0^{\circ})=1\).
02

Calculate the work done

Since \(\cos\theta=1\), we can simplify the formula for work done as the following: $$ W = F \cdot d $$ In our problem, the distance moved in the direction of the force is the length \(l\) by which the wire stretches. So we can substitute \(d\) with \(l\): $$ W = F \cdot l $$ Therefore, the work done in stretching the wire is given by the option (B) \(F l\).

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