You hang a flood lamp from the end of a vertical steel wire. The flood...
F/A = e/L
F/A = 0.18/l ( let the length be l)
F/A = x/2l
0.18/L = x/2l
0.18×2l = xl
0.36l = xl
x = 0.36
View all questions of this test
You hang a flood lamp from the end of a vertical steel wire. The flood...
Given: The flood lamp stretches the wire by 0.18 mm, and stress is proportional to strain.
To find: How much would the wire stretch if it were twice as long.
Solution:
Let us assume the original length of the wire as L and the elongation produced by the flood lamp as δL.
According to Hooke's law, stress is proportional to strain.
Hence, Stress/Strain = Constant (K)
Let us assume the constant K as k.
Therefore, Stress = k × Strain
The strain is given by the formula,
Strain (ε) = δL/L
Stress (σ) = F/A
where F is the force applied, and A is the cross-sectional area of the wire.
As the wire is hanging vertically, the force acting on the wire is its weight, which is given by:
F = mg
where m is the mass of the lamp, and g is the acceleration due to gravity.
Hence, the strain can be calculated as follows:
Strain (ε) = δL/L = σ/k
σ = F/A = mg/A
Thus, we have:
δL/L = σ/k = (mg/A)/k
δL = (mgL/kA)
As the stress is proportional to strain, we can write:
δL/L = K1
where K1 is the constant of proportionality.
Thus, we have:
K1 = δL/L = (mgL/kA)
Now, we need to find the elongation produced when the length of the wire is doubled.
Let the new length of the wire be 2L.
The new cross-sectional area of the wire is the same as the original one.
Hence, the new elongation produced can be calculated as follows:
δL' = K1 × 2L = 2K1L
δL' = 2(δL/L)L
δL' = 2(0.18mm/1m)1m
δL' = 0.36mm
Therefore, the wire would stretch by 0.36 mm if it were twice as long.
Hence, option (A) is the correct answer.
You hang a flood lamp from the end of a vertical steel wire. The flood...
F/A=e/L
F/A=0.18/l ( let the length be l)
F/A=x/2l
0.18/L=x/2l
0.18×2l=xl
0.36l=xl
x=0.36
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.