At 0-C a steel rod of square cross-section of side -2 cm is rigidly clamped at both ends so that its length cannot change- lf the Young-s modulus of steel is 20- 1010 N-m2 and the linear coefficient is 12- 10-6-oC- then the force exerted on the clamps if the temperature is raised to 20oC is

The correct option is C 9600 NAccording to Concept of #160;linear #160;expansion and Young's Modulus F = A Y α #160;Δ #160;Δ t F = 2 × #160 ...

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Standard XII

Physics

Longitudinal Strain

At 0∘C a st...

Question

At $0^{\circ} C$ a steel rod of square cross-section of side $\sqrt{2}$ cm is rigidly clamped at both ends so that its length cannot change. lf the Young's modulus of steel is $20 \times 10^{10} N / m^{2}$ and the linear coefficient is $12 \times 10^{- 6} /^{o} C$ , then the force exerted on the clamps if the temperature is raised to $20^{o} C$ is

2400 N

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4800 N

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9600 N

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7200 N

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Solution

The correct option is C 9600 N
According to Concept of linear expansion and Young's Modulus
$F = A Y α Δ Δ t$
$F = 2 \times 10^{- 4} \times 20 \times 10^{10} \times 12 \times 10^{- 6} \times (20 - 0)$
$F = 9600 N$

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Q. A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will the rod exert on one of the clamps? Area of cross-section of the rod is 2.00 mm². Coefficient of linear expansion of steel is 12.0 × 10^–6 °C^–1 and Young's modulus of steel is 2.00 × 10¹¹ Nm^–2.

A steel rod is rigidly clamped at its two ends. The rod is under zero tension at $20^{\circ} C$ . If the temperature rises to $100^{\circ} C$ , what force will the rod exert on one of the clamps? Area of cross section of the rod = $2.0 m m^{2}$ . Coefficient of linear expansion of steel $= 12.0 \times 10^{- 6}^{\circ} C^{- 1}$ and Young's modulus of steel = $2.00 \times 10^{11} N m^{- 2}$ .

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A uniform steel wire of cross-sectional area $0.20 m m^{2}$ is held fixed by clamping its two ends. Find the extra force exerted by each clamp on the wire if the wire is cooled from $100^{\circ} C$ to $0^{\circ} C$ . Young's modulus of steel = $2.0 \times 10^{11} N / m^{2}$ . Coefficient of linear expansion of steel = $1.2 \times 10^{- 5} /^{\circ} C$ .

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At 0∘C a steel rod of square cross-section of side √2 cm is rigidly clamped at both ends so that its length cannot change. lf the Young's modulus of steel is 20×1010N/m2 and the linear coefficient is 12×10−6/oC, then the force exerted on the clamps if the temperature is raised to 20oC is

The correct option is C 9600 NAccording to Concept of linear expansion and Young's ModulusF=AYαΔΔtF=2×10−4×20×1010×12×10−6×(20−0)F=9600N

The correct option is C 9600 N
According to Concept of linear expansion and Young's Modulus
$F = A Y α Δ Δ t$
$F = 2 \times 10^{- 4} \times 20 \times 10^{10} \times 12 \times 10^{- 6} \times (20 - 0)$
$F = 9600 N$