A wire of cross-sectional are 3 mm2 is first stretched between two fixed points at a temperature of 20-C- Determine the tension when the temperature falls to 10-C- Coefficient of linear expansion - -10-5 -C-1 and Y-2- 1011N-m2 -

The correct option is C 60 N Δ ll = αΔ T Δ T = 20^o #160;C 10^o #160;C = 10^o #160;C T = YΔ l Al = YA αΔ T = 2 × 10^11× 3 × 10^ 6× 10^ ...

You visited us 7 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Distance

A wire of cro...

Question

A wire of cross-sectional are 3 $m m^{2}$ is first stretched between two fixed points at a temperature of $20^{\circ} C$ . Determine the tension when the temperature falls to $10^{\circ} C$ . Coefficient of linear expansion
$α = 10^{- 5}^{\circ} C^{- 1}$ and $Y = 2 \times 10^{11} N / m^{2}$ :-

20 N

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

30 N

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

60 N

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

120 N

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

Open in App

Solution

The correct option is C 60 N
$\frac{Δ l}{l} = α Δ T$
$Δ T = 20^{o} C - 10^{o} C = 10^{o} C$
$T = \frac{Y Δ l A}{l} = Y A α Δ T = 2 \times 10^{11} \times 3 \times 10^{- 6} \times 10^{- 5} \times 10 = 60 N$

Suggest Corrections

Similar questions

Q. A steel wire of cross-sectional area

0.5 m m^{2}

is held between two fixed supports. If the wire is just taut at

20^{\circ} C

, determine the tension when the temperature falls to

0^{\circ} C

. Coefficient of linear expansion of steel is

1.2 \times 10^{- 5} /^{\circ} C

and its Young's modulus is

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

Q. A steel wire of cross-sectional area 0.5 mm²is held between two fixed supports. If the wire is just taut at 20°C, determine the tension when the temperature falls to 0°C. Coefficient of linear expansion of steel is 1.2 × 10^–5 °C^–1 and its Young's modulus is 2.0 × 10^–11 Nm^–2.

Q. A tungsten wire,

0.5 m m

in diameter is just stretched between two fixed point at a temperature

40^{o}

C. Determine the tension in the wire when the temperature falls to

20^{o} C

.(coefficient of linear expansion of tungsten =

4.5 \times 10^{- 6} /^{o} C

;Young's modulus of tungsten

= 3.45 \times 10^{10} N m^{- 2}

)

Q. A steel wire of uniform cross - sectional area

2 m m^{2}

is heated up to

50^{\circ} C

and is stretched by clamping its two ends rigidly. The change in tension when the temperature falls from

50^{\circ}

C to

30^{\circ}

C is

(coefficient of linear expansion α = 1.1 \times 10^{- 5} /^{\circ} C, Youngs modulus Y = 2.0 \times 10^{11} \frac{N}{m^{2}})

Q. A steel wire of cross section area

0.5 m m^{2}

is held between two fixed supports. If the tension in the wire is negligible, and it is just taut at a temperature of

20^{\circ} C

determine the tension when the temperature falls to

0^{\circ} C

. Assume the distance between supports to be the same,Young's modulus of steel

Y = 2.1 \times 10^{12}

dynes and coefficient of linear expansion for steel

α = 12 \times 10^{- 6}^{\circ} C^{- 1}

Join BYJU'S Learning Program

A wire of cross-sectional are 3 mm2 is first stretched between two fixed points at a temperature of 20∘C. Determine the tension when the temperature falls to 10∘C. Coefficient of linear expansion α=10−5∘C−1 and Y=2×1011N/m2 :-

The correct option is C 60 NΔll=αΔTΔT=20oC−10oC=10oCT=YΔlAl=YAαΔT=2×1011×3×10−6×10−5×10=60N

A wire of cross-sectional are 3 $m m^{2}$ is first stretched between two fixed points at a temperature of $20^{\circ} C$ . Determine the tension when the temperature falls to $10^{\circ} C$ . Coefficient of linear expansion
$α = 10^{- 5}^{\circ} C^{- 1}$ and $Y = 2 \times 10^{11} N / m^{2}$ :-

The correct option is C 60 N
$\frac{Δ l}{l} = α Δ T$
$Δ T = 20^{o} C - 10^{o} C = 10^{o} C$
$T = \frac{Y Δ l A}{l} = Y A α Δ T = 2 \times 10^{11} \times 3 \times 10^{- 6} \times 10^{- 5} \times 10 = 60 N$