A thin rod of negligible mass and area of cross-section 2 - 10-5m2- suspended vertically from one end- has a length of 0-5 m at 200-C- The rod is cooled to 0-C- but length is kept same by attaching a mass at the lower end- The value of this mass is Young-s modulus -1011 N-m2- Coefficient of linear expansion 10-5 K-1-

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Byju's Answer

Standard XII

Physics

Bernoulli's Principle

A thin rod of...

Question

A thin rod of negligible mass and area of cross-section $2 * 10^{- 5} m^{2}$ , suspended vertically from one end, has a length of 0.5 m at $200^{\circ}$ C. The rod is cooled to $0^{\circ}$ C, but length is kept same by attaching a mass at the lower end. The value of this mass is (Young's modulus $= 10^{11} N / m^{2}$ , Coefficient of linear expansion $10^{- 5} K^{- 1}$ ).

20 kg

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30 kg

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40 kg

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50 kg

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Answer Required

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Solution

The correct option is E 40 kg
Tension developed in the rod will be $T = A (Y α Δ T) = (2 X 10^{- 5}) (10^{11}) (10^{- 5}) (200) = 4000 N$

This needs to be balanced by the weight, hence,

$4000 = m g$

$m = 40 k g$

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The correct option is E 40 kgTension developed in the rod will be T=A(YαΔT)=(2X10−5)(1011)(10−5)(200)=4000NThis needs to be balanced by the weight, hence,4000=mgm=40kg

The correct option is E 40 kg
Tension developed in the rod will be $T = A (Y α Δ T) = (2 X 10^{- 5}) (10^{11}) (10^{- 5}) (200) = 4000 N$

This needs to be balanced by the weight, hence,

$4000 = m g$

$m = 40 k g$