You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Thermal Expansion

Two wires P a...

Question

Two wires P and Q of same cross-sectional area $A = 10 m m^{2}$ and the same length $l_{0} = 1$ m but made of different materials are joined together and their ends are rigidly clamp between two walls with negligible tension. Their respective Young's modulus and the coefficients of linear expansion are $Y_{1}, α_{1}$ and $Y_{2}, α_{2}$ respectively.
Given $Y_{1} = 2 \times 10^{9} N / m^{2}, α_{1} = 3 \times 10^{- 4} /^{\circ} C, Y_{2} = 10^{9} N / m^{2}, α_{2} = 6 \times 10^{- 4} /^{\circ} C$ ,

If the temperature of system is reduced by $20^{\circ} C$ the tension developed in wire P is

60 N

No worries! We‘ve got your back. Try BYJU‘S free classes today!

120 N

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

40 N

No worries! We‘ve got your back. Try BYJU‘S free classes today!

180 N

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
120 N

If F is the horizontal force on the wire, then

$(\frac{E l_{0}}{A Y_{1}} + \frac{F l_{0}}{F Y_{2}}) = α_{1} Δ T + α_{2} Δ T$

Putting values gives F = 120 N.

Suggest Corrections

Similar questions

Two wires P and Q of same cross-sectional area $A = 10 m m^{2}$ and the same length $l_{0} = 1$ m but made of different materials are joined together and their ends are rigidly clamp between two walls with negligible tension. Their respective Young's modulus and the coefficients of linear expansion are as $Y_{1}, α_{1}$ and $Y_{2}, α_{2}$ respectively.
Given $Y_{1} = 2 \times 10^{9} N / m^{2}, α_{1} = 3 \times 10^{- 4} /^{\circ} C, Y_{2} = 10^{9} N / m^{2}, α_{2} = 6 \times 10^{- 4} /^{\circ} C$ ,

Displacement of joint O is

Two rods of different materials having coefficients of thermal expansion $α_{1}$ and $α_{2}$ and Young's modulii $Y_{1}$ and $Y_{2}$ are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

Q. Two wires

A

and

B

of the same cross-sectional areas, Young's modulii

Y_{1}

and

Y_{2}

and coefficients of linear expansion

α_{1}

and

α_{2}

respectively, are joined together and fixed between rigid supports at either ends at

0^{\circ} C

. The tension in the compound wire when wire

A

is heated to temperature

T_{1}

and wire

B

is cooled to temperature

T_{2}

is equal to tension in the compund wire when only wire

A

is cooled to temperature

T_{2}

. Find the correct option.

Q. Two rods of different materials having coefficients of linear expansions

α_{1}

and

α_{2}

and young's modulus of elasticity

Y_{1}

and

Y_{2}

respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature without bending. If

α_{1} : α_{2} = 2 : 3,

then the thermal stress developed in the two rods will be equal if

Y_{1} : Y_{2}

is equal to

Two rods of different materials, having coefficients of linear expansion $α_{1}$ and $α_{2}$ and Young's moduli $Y_{1}$ and $Y_{2}$ respectively, are fixed between two rigid walls. The rods are heated to the same temperature. There is no bending of the rods. If $α_{1} : α_{2} = 2 : 3$ , the thermal stress developed in the two rods will be equal provided $Y_{1} : Y_{2}$ is equal to

Join BYJU'S Learning Program

The correct option is B 120 N If F is the horizontal force on the wire, then (El0AY1+Fl0FY2)=α1ΔT+α2ΔT Putting values gives F = 120 N.

The correct option is B
120 N

If F is the horizontal force on the wire, then

$(\frac{E l_{0}}{A Y_{1}} + \frac{F l_{0}}{F Y_{2}}) = α_{1} Δ T + α_{2} Δ T$

Putting values gives F = 120 N.