Question

A wire of length L is hanging from a fixed support The length changes to L1 and L2 when masses M1 and M2 are suspended respectively from its free end. Then L is equal to

Answer 1

Answer:

d will be the correct answer

Answer 2

The value of L is $\dfrac{M_{1}}{M_{2}}(l_{1}-l_{2})+l_{1}$

Explanation:

Given that,

Length = L

The length changes L₁ and L₂ when masses M₁ and M₂ are suspended respectively from its free end

We know that,

The young's modulus is

$y=\dfrac{MgL}{A(l_{1}-L)}$

We need to calculate the value of L

Using formula of young's modulus

For first case,

$y_{1}=\dfrac{M_{1}gL}{A(l_{1}-L)}$....(I)

For second case,

$y_{2}=\dfrac{(M_{1}+M_{2})gL}{A(l_{2}-L)}$....(II)

From equation (I) and (II)

$\dfrac{M_{1}gl}{A(L_{1}-l)}=\dfrac{(M_{1}+M_{2})gL}{A(l_{2}-L)}$

$M_{1}l_{2}-M_{1}l=M_{1}l_{1}-M_{1}L+M_{2}l_{1}-M_{2}L$

$M_{1}l_{2}=M_{1}l_{1}+M_{2}l_{1}-M_{2}L$

$M_{2}L=M_{1}(l_{1}-l_{2})+M_{2}l_{1}$

$L=\dfrac{M_{1}}{M_{2}}(l_{1}-l_{2})+l_{1}$

Hence, The value of L is $\dfrac{M_{1}}{M_{2}}(l_{1}-l_{2})+l_{1}$

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Topic : young's modulus

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