The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

  • Option 1)

    2:1

  • Option 2)

    4:1

  • Option 3)

    1:1

  • Option 4)

    1:2

 

Answers (1)

As learnt

Young Modulus -

Ratio of normal stress to longitudnal strain

it denoted by Y

Y= frac{Normal : stress}{longitudnal: strain}

- wherein

Y=frac{F/A}{Delta l/L}

F -  applied force

A -  Area

Delta l -  Change in lenght

l - original length

 

 

 

 Y_{steel}=2 Y_{brass}

l_{steel}=l_{brass}

A_{steel}=A_{brass}

Y=\frac{Fl}{A \: \Delta l} \: \: \: or \: \: \: \Delta l= \frac{Fl}{AY}

According to question,

\Delta l_{steel}=\Delta l_{brass} \: \: \: \Rightarrow \left ( \frac{F}{Y} \right )_{steel}= \left ( \frac{F}{Y} \right )_{brass}

\frac{F_{steel}}{F_{brass}}=\frac{Y_{steel}}{Y_{brass}}=2:1


Option 1)

2:1

This option is correct

Option 2)

4:1

This option is incorrect

Option 3)

1:1

This option is incorrect

Option 4)

1:2

This option is incorrect

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