Answer

Verified

345.6k+ views

**Hint:**In order to find tensions in wires , we need to balance the all forces acting on three wires and weight acting on ceiling in downward direction and in order to achieve the same length in all three wires their change in length must be the same.

**Complete step by step answer:**

Let ${F_1}$ , ${F_2}$ and ${F_3}$ be the tension forces on three wires respectively. And their change in length is denoted as \[\Delta {L_1}\] , $\Delta {L_2}$ and $\Delta {L_3}$ .Now, balancing all three forces with force of gravity as;

${F_1} + {F_2} + {F_3} = 300 \times 9.8$

$\Rightarrow {F_1} + {F_2} + {F_3} = 2940$

And also, ${F_1} = {F_3}$ so we can write,

${F_2} = 2940 - 2{F_1} \to (i)$

And we also know that, from modulus of elasticity of steel as given

\[{F_1} = {F_3} = {F_2} + \dfrac{{dAE}}{L}\]

\[\Rightarrow {F_1} = {F_2} + \dfrac{{dAE}}{L}\]

Put, the value of ${F_2}$ from equation $(i)$ in above equation, we get

$3{F_1} = 2940 + \dfrac{{dAE}}{L} \to (ii)$

Here we have given that,

$d = 6\,mm = 0.006\,m$

$\Rightarrow A = 2 \times {10^{ - 6}}\,{m^2}$

$\Rightarrow E = 200 \times {10^9}\,N{m^{ - 2}}$

$\Rightarrow L = 2\,m$

On putting these parameters value in equation $(ii)$ we get,

$3{F_1} = 2940 + \dfrac{{6 \times 2 \times 200}}{2}$

$\Rightarrow 3{F_1} = 2940 + 1200$

$\Rightarrow {F_1} = \dfrac{{4140}}{3}$

$\therefore {F_1} = 1380\,N$

**Hence tension in the wire $1$ is ${F_1} = 1380\,N$.**

(b) Now, simply from equation $(i)$ we have,

${F_2} = 2940 - 2{F_1}$

Put ${F_1} = 1380\,N$ in above equation we get,

${F_2} = 2940 - 2760$

$\therefore {F_2} = 180\,N$

**Hence, the tension in wire $2$ is ${F_2} = 180N$.**

**Note:**Remember, all the tension forces on three wires are acting in the upward direction and the weight of the cylinder is downward direction. And the ceiling is in equilibrium state that’s why changes in all three wires length will be the same and hence balancing the wires and cylinder. Also $g = 9.8m{\sec ^{ - 2}}$ and $1mm = {10^{ - 3}}m$.

Recently Updated Pages

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

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

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

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

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

Write a letter to the principal requesting him to grant class 10 english CBSE