You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Shear Modulus

Two rods of d...

Question

Two rods of different materials and identical cross sectional area, are joined face to face at one end and their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by $30^{o} C$ , the magnitude of the displacement of the joint of the rod is (length of rods $l_{1} = l_{2} = 1$ unit, ratio of their young's moduli $Y_{1} / Y_{2} = 2$ , coefficient of linear expansion are $α_{1}$ and $α_{2}$ )

5 (α_{2} - α_{1})

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

10 (α_{1} - α_{21})

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

10 (α_{2} - {2 α}_{1})

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

5 ({2 α}_{1} - α_{2})

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

Open in App

Solution

The correct option is C $10 (α_{2} - {2 α}_{1})$
$l_{1} α_{2} △ θ + l_{2} α_{2} △ θ = \frac{F_{1} l_{2}}{A_{1} y_{2}} + \frac{f_{2} l_{2}}{A_{2} y_{2}}$
$1 + α_{1} \times 30 + 1 \times α_{2} \times 30 = \frac{F \times 1}{A \times 2 y} + \frac{F \times 1}{A \times y}$
[where , $y_{1}$ & $y_{2}$ are young's modulus $\frac{y_{1}}{y_{2}} = 2]$
$30 (α_{1} + α_{2}) = \frac{3 F}{2 A y}$
$10 (α_{1} + α_{2}) = \frac{F}{2 A y}$
Thus, displacement of joint is
$\frac{F_{1} l_{1}}{A y_{1}} - l_{2} α_{1} △ θ = \frac{F \times l_{1}}{A_{1} y_{2}} - 1 \times α_{1} \times 30 = 10 (α_{1} + α_{2}) - 30 α_{1}$
$= 10 (α_{2} - 2 α_{1})$

Suggest Corrections

Similar questions

Q. Two rods of different materials with coefficients of thermal expansion

α_{1}

and

α_{2}

respectively; Young's moduli

Y_{1}

and

Y_{2}

respectively; of initial lengths

l_{1}

and

l_{2}

respectively of equal cross-sectional areas are joined at one end. The free ends are fixed to two vertical walls as shown in figure.
Temperature of the surrounding is then increased by

T^{\circ} C

. Find out the displacement of the joint of the rods.

Q. Two rods of different materials and of equal cross-sectional areas and length

1 m

are joined face to face at one end and their free ends are fixed to rigid walls. If the temperature of the surrounding is increased by

30^{\circ} C

, the magnitude of the displacement of the joint of the rods is :

[α_{1} = 2 \times 10^{- 5}^{\circ} C^{- 1}, α_{2} = 5 \times 10^{- 5}^{\circ} C^{- 1},

Y_{1} = 2 \times 10^{10} {N/m}^{2}, Y_{2} = 10^{10} {N/m}^{2}]

Q. Two rods of different materials and of equal cross-sectional areas and length

1 m

are joined face to face at one end and their free ends are fixed to rigid walls. If the temperature of the surrounding is increased by

30^{\circ} C

, the magnitude of the displacement of the joint of the rods is :

[α_{1} = 2 \times 10^{- 5}^{\circ} C^{- 1}, α_{2} = 5 \times 10^{- 5}^{\circ} C^{- 1},

Y_{1} = 2 \times 10^{10} {N/m}^{2}, Y_{2} = 10^{10} {N/m}^{2}]

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

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

Join BYJU'S Learning Program