Question

A uniform rectangular block of mass of 50 kg is hung horizontally with the help of three wires A, B and C each of length and area of 2m and 10mm² respectively as shown in the figure. The central wire is passing through the centre of gravity and is made of material of Young's modulus 7.5 x 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: 

Options

• 1 : 3

• 4 : 3

• 5 : 3

• 7 : 3

Answer 1

4 : 3

Explanation:

Given, L_A = L_B = L_C  and  A_A = A_B = A_C 

∴ L = 2m

A = 10 mm²

As the block is hanging horizontally, the extension produced in each wire would be the same 

i.e. l = I_A = l_B = l_C.

we know,

Y = ${\displaystyle \frac{\text{FL}}{\text{Al}}}$

Here, Y_B = 7.5 × 10¹⁰ N/m²

Y_A = Y_C = 10¹¹ N/m² 
∴ ${\displaystyle \frac{{\text{Y}}_{\text{A}}}{{\text{Y}}_{\text{B}}}=\frac{{\text{F}}_{\text{A}}\text{L}}{\text{Al}}\times \frac{\text{Al}}{{\text{F}}_{\text{B}}\text{L}}}$

⇒ ${\displaystyle \frac{{\text{Y}}_{\text{A}}}{{\text{Y}}_{\text{B}}}=\frac{{10}^{11}}{7.5\times {10}^{10}}=\frac{4}{3}}$

∴ Tension in wires A and B are in the ratio 4 : 3