Advertisements
Advertisements
Question
Long answer type question.
Describe an experiment to find out Young’s modulus of the material in the form of a long string wire.
Solution
Experimental description to find Young’s modulus:
- Consider a metal wire suspended from a rigid support. A load is attached to the free end of the wire. Due to this, the deforming force gets applied to the free end of wire in downward direction and it produces a change in length.
Let,
L = original length of wire,
Mg = weight suspended to wire,
l = extension or elongation,
(L + l) = new length of wire
r = radius of the cross-section of wire - In its equilibrium position,
`"Longitudinal stress" = "Applied force"/"Area of cross section"`
`= "F"/"A"`
`= "Mg"/(pi"r"^2)`
`"Longitudinal strain" = "Change in length"/"Original length" = l/"L"` - From definition,
`"Young’s modulus (Y)" = "longitudinal stress"/"longitudinal strain"`
`= ("Mg"//pi"r"^2)/(l//"L")`
∴ Y = `"Mg L"/(pi"r"^2 l)`
APPEARS IN
RELATED QUESTIONS
Answer in one sentence.
What is Young’s modulus of a rigid body?
Answer in one sentence.
Define Poisson’s ratio.
Answer the following:
What is Young’s modulus?
Answer the following.
A wire gets stretched by 4 mm due to a certain load. If the same load is applied to a wire of same material with half the length and double the diameter of the first wire, what will be the change in its length?
Answer the following.
A solid metal sphere of volume 0.31 m3 is dropped in an ocean where water pressure is 2 × 107 N/m2. Calculate change in volume of the sphere if the bulk modulus of the metal is 6.1 × 1010 N/m2.
Answer the following.
A wire of mild steel having an initial length 1.5 m and diameter 0.60 mm gets extended by 6.3 mm when a certain force is applied to it. If Young’s modulus of mild steel is 2.1 × 1011 N/m2, calculate force applied.
Answer the following.
A composite wire is prepared by joining a tungsten wire and steel wire end to end. Both the wires are of the same length and the same area of cross-section. If this composite wire is suspended to a rigid support and a force is applied to its free end, it gets extended by 3.25 mm. Calculate the increase in the length of tungsten wire and steel wire separately.
`("Y"_"Tungsten"= 4.1 × 10^11 "Pa, Y"_"Steel"= 2 × 10^11 "Pa")`
A steel wire having a cross-sectional area of 1.2 mm2 is stretched by a force of 120 N. If a lateral strain of 1.455 is produced in the wire, calculate the Poisson’s ratio.
(Given: YSteel = 2 × 1011 N/m2)
A telephone wire 125 m long and 1 mm in radius is stretched to a length 125.25 m when a force of 800 N is applied. What is the value of Young’s modulus for the material of wire?
A rubber band originally 30 cm long is stretched to a length of 32 cm by a certain load. What is the strain produced?
Answer the following.
What is the stress in a wire which is 50m long and 0.01 cm2 in cross-section, if the wire bears a load of 100 kg?
Answer the following.
What is the strain in a wire cable of the original length 50 m whose length increases by 2.5 cm when a load is lifted?
For homogeneous isotropic material, which one of the following cannot be the value of Poisson's ratio?
