A homogeneous block with a mass m hangs on three vertical wires of equal length arranged symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of copper.All the wires have the same cross-section. Consider the modulus of elasticity of steel to be double than that of copper.

Open in App

Solution

Given : $Δ L_{s} = Δ L_{c}$ $Y_{s} = 2 Y_{c}$ $L_{s} = L_{c}$
Using $Y = \frac{T L}{A Δ L}$ $⟹ Δ L = \frac{T L}{A Y}$

$∴$ $Δ L_{s} = \frac{T_{s} L_{s}}{A_{s} Y_{s}}$ and $Δ L_{c} = \frac{T_{c} L_{c}}{A_{c} Y_{c}}$

But $Δ L_{c} = Δ L_{s}$ i.e $\frac{T_{s} L_{s}}{A_{s} (2 Y_{c})} = \frac{T_{c} L_{c}}{A_{c} Y_{c}}$
$⟹$ $T_{s} = 2 T_{c}$

Also $2 T_{c} + T_{s} = m g$
OR $2 T_{c} + 2 T_{c} = m g$ $⟹ T_{c} = \frac{m g}{4}$
$⟹$ $T_{s} = \frac{m g}{2}$

Suggest Corrections

Similar questions

A heavy plank of mass 100 kg hangs on three vertical wires of equal length arranged symmetrically (see fig.). The middle wire is of steel and the other two are of copper. All the wires have the same cross-section. The modulus of elasticity of steel is twice that of copper. The tensions in the copper and steel wires are respectively

Q. Two wire of same radius and length are subjected to the same load, One wire is of steel and the other is copper. If Young's modulus of steel is twice that of copper, then the ratio of elastic energy stored per unit volume of steel to that of copper wire is

Two wires of equal cross section but one made of steel and the other of copper are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. Find the ratio of the lengths of the two wires. Young modulus of steel = 2.0 x 10¹¹ N m^-2 and that of copper = 1.1 x 10¹¹ N m^-2.

A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension.

The ratio of stresses developed in the two wires is:

c o p p e r s t e e l

Q. Two wires of equal cross-section but one made of steel and the other of copper, are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. The ratio of the lengths of the two wires is found to be

\frac{10 n}{11}

. Then, the value of

n

Young’s modulus of steel

= 2.0 \times 10^{11} {N/m}^{2}

and that of copper

= 1.1 \times 10^{11} {N/m}^{2}

Join BYJU'S Learning Program

Given : ΔLs=ΔLc Ys=2Yc Ls=LcUsing Y=TLAΔL ⟹ΔL=TLAY∴ ΔLs=TsLsAsYs and ΔLc=TcLcAcYcBut ΔLc=ΔLs i.e TsLsAs(2Yc)=TcLcAcYc⟹ Ts=2Tc Also 2Tc+Ts=mgOR 2Tc+2Tc=mg ⟹Tc=mg4⟹ Ts=mg2