Calculate the work done in stretching steel wire of length 2m and of cross sectional area 0.0225 mm², when a load of 100 N is applied slowly to its free end. ( Young's modulus of steel = 20 x 10¹⁰ N / m²) (Ans: 2.222 J)
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given, cross sectional area, A = 0.0225 mm² = 0.0225 × 10^-6 m²
Length of wire, l = 2m
Load , F = 100N
we know, Y = Fl/A∆l
where F is load , l is length of wire, A is cross sectional area of wire and ∆l is extension of wire.
so, ∆l = Fl/AY
= 100 × 2/(0.0225 × 10^-6 × 20 × 10^10 ) = 4.444 × 10^-2 m
Now, workdone = 1/2 × load × extension of wire
= 1/2 × 100 × 4.444 × 10^-2
= 2.222J
hence, workdone = 2.222J
Length of wire, l = 2m
Load , F = 100N
we know, Y = Fl/A∆l
where F is load , l is length of wire, A is cross sectional area of wire and ∆l is extension of wire.
so, ∆l = Fl/AY
= 100 × 2/(0.0225 × 10^-6 × 20 × 10^10 ) = 4.444 × 10^-2 m
Now, workdone = 1/2 × load × extension of wire
= 1/2 × 100 × 4.444 × 10^-2
= 2.222J
hence, workdone = 2.222J
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