A steel wire of length 20 cm and cross section 1mm^2 is tied rigidly at both ends at the room temperature 30C. If the temperature falls to 10C , what will be the change in tension ? given Y=2×10^11Nm-2 and coefficient of linear expansion 1.1×10^-5 /C PLZZZ SMONE ANSWER TO THIS QUESTION.?

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A steel wire of length 20 cm and cross section 1mm^2 is tied rigidly a...

Formula of youngs modulus.. Apply it deepthi.. And root T/m/l... Means T/meu..

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A steel wire of length 20 cm and cross section 1mm^2 is tied rigidly a...

Problem Statement:
A steel wire of length 20 cm and cross-section 1mm^2 is tied rigidly at both ends at a room temperature of 30°C. If the temperature falls to 10°C, what will be the change in tension? Given Young's modulus (Y) = 2×10^11 Nm^-2 and the coefficient of linear expansion (α) = 1.1×10^-5 /°C.

Solution:
To find the change in tension of the steel wire when the temperature falls from 30°C to 10°C, we can use the equation:

ΔTension = Tension_final - Tension_initial

To calculate the initial tension in the wire, we can use the formula for tension:

Tension_initial = (Force_initial / Area)

Step 1: Calculate the initial tension:
To find the initial force, we need to calculate the initial length of the wire. Since the wire is tied rigidly at both ends, the initial length is equal to the original length.

Initial length (L_initial) = 20 cm = 0.2 m

Using the formula for linear expansion, we can calculate the change in length:

ΔL = α * L_initial * ΔT

ΔT = (Final temperature - Initial temperature) = (10°C - 30°C) = -20°C

ΔL = (1.1×10^-5 /°C) * (0.2 m) * (-20°C) = -4.4×10^-5 m

The change in length is negative because the temperature is decreasing.

The initial length of the wire (L_initial) remains the same, so the final length (L_final) can be calculated as:

L_final = L_initial + ΔL = 0.2 m - 4.4×10^-5 m = 0.199956 m

Step 2: Calculate the initial tension:
The initial tension can be calculated using the formula:

Tension_initial = (Force_initial / Area)

The area of the cross-section is given as 1 mm^2 = 1×10^-6 m^2

Tension_initial = (Force_initial / (1×10^-6 m^2))

Step 3: Calculate the final tension:
To calculate the final tension, we need to find the final force. The final force can be calculated using the final length of the wire (L_final) and the Young's modulus (Y):

Force_final = Y * (ΔL / L_initial) * (Area)

Force_final = (2×10^11 Nm^-2) * (-4.4×10^-5 m / 0.2 m) * (1×10^-6 m^2)

Step 4: Calculate the change in tension:
Now we can calculate the change in tension using the formula:

ΔTension = Tension_final - Tension_initial

ΔTension = (Force_final / (1×10^-6 m^2)) - (Force_initial / (1×10^-6 m^2))

Simplifying the equation, we get:

ΔTension = (Force_final - Force_initial) / (1×10^-6 m^2)

Substituting the values of Force

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