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Mechanical Properties Of Solids

Question
CBSEENPH11026456
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Young's modulus for a steel wire is 2 x 1011 Pa and its elastic limit is 2.5 x 108 Pa. By how much can a steel wire 3 m long and 2 mm in diameter be stretched before the elastic limit is exceeded?

  • 3.75  mm

  • 7.50 mm

  • 4.75 mm

  • 4.00 mm

Solution

A.

3.75  mm

The cross-sectional area of a wire of radius r = l mm= 10-3m is  A = π r2 = 3.14 x 10-6 m2.
The maximum force that can be applied without exceeding the elastic limit is therefore

          F = FAmax × A

          F = (2.5 × 108 N m-2 ) ( 3.14 × 10-6 m2 )

           F = 785 N

When this force is applied, the wire will stretch by

          ΔL = LY FA

                = 3 m 785 N2 × 1011 Nm2 3.14 × 10-6 m2

                 = 3.75 × 10-3 m

            ΔL = 3.75 mm

Some More Questions From Mechanical Properties of Solids Chapter

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

Assertion:  A rigid body can be elastic.

Reason: If s force is applied on the rigid, its dimensions may change.

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