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A uniform rectangular block of mass 50 kg is hung horizontally with the help of three wires A, B and C each of length and area of 2 m and 10 mm² respectively as shown in the figure. The central wire is passing through the centre of gravity and is made of a material of Young's modulus 7.5 × 10¹⁰ Nm^–2 and the other two wires A and C symmetrically placed on either side of the wire B are of Young's modulus 10¹¹ Nm^–2. The tension in the wires A and B will be in the ratio of

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1 : 3

4 : 3

5 : 3

7 : 3

answer is B.

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Detailed Solution

The extension is same is all three wires, as the block will remain horizontal.

$e_{A} = e_{B} = e_{C} \Rightarrow \frac{F_{A} l}{{AY}_{A}} = \frac{F_{B} l}{{AY}_{B}}$

$\Rightarrow \frac{F_{A}}{F_{B}} = \frac{Y_{A}}{Y_{B}} = \frac{10^{11}}{7.5 x 10^{10}} = \frac{10}{7.5} = \frac{4}{3}$

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