Answer

Verified

428.7k+ views

**Hint**When the temperature of a solid body drops, it decreases in length due to length contraction. We must provide an amount of force that will compensate for the decrease in length of the rod by providing lateral stress on the rod. So we need to calculate this stress by the formula using the coefficient of linear expansion and the young’s modulus of the wire.

In the solution we will be using the following formula,

$\Rightarrow \Delta L = L\alpha \Delta T $ where $ \Delta L $ is the change in length of the rod of length $ L $ , coefficient of linear expansion $ \alpha = {10^{ - 5}}/^\circ C $ due to temperature change $ \Delta T $

$\Rightarrow Y = \dfrac{{TL}}{{A\Delta L}} $ where $ Y $ is the young’s modulus, $ T $ is the tension in the rod, $ A $ is the cross-sectional area of the rod.

**Complete step by step answer**

We know that when the temperature of the rod drops, its length will decrease according to the equation

$\Rightarrow \Delta L = L\alpha \Delta T $

Substituting the values of $ \alpha = 0.000011 $ and $ \Delta T = (15 - 60) = - 45 $ , we get

$\Rightarrow \Delta L = L(0.000011 \times 45) $

$\Rightarrow 0.000495L $

Now to keep the rod at the same length, we must provide enough force that can increase the length of the rod by the same amount. So, substituting the value of $ \Delta L $ in the equation of young’s modulus $ Y = \dfrac{{TL}}{{A\Delta L}} $ , we get

$\Rightarrow Y = \dfrac{{TL}}{{A0.000495L}} $

Substituting the value of $ A = 1m{m^2} = {10^{ - 6}}{m^2} $ and $ Y = 2 \times {10^{11}} $ ,we get

$\Rightarrow 2 \times {10^{11}} = \dfrac{T}{{{{10}^{ - 6}} \times 0.000495}} $

Solving for $ T $ , we get

**$ T = 99\,N $ which corresponds to option (D).**

**Note**

Here we have assumed that the decrease in length occurs almost instantaneously however in reality, the temperature of the rod will decrease at a slow rate and so its length will decrease gradually as well. So, we must increase the force applied on the rod gradually too otherwise we might over-extend the rod in length. While we don’t know the length of the rod, it isn’t needed in the final solution since it cancels out and the force that we must apply is independent of the length of the rod.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths