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Standard XII

Physics

Thermal Expansion

A thin rod of...

Question

A thin rod of negligible mass and cross-sectional area 4x10 $^{- 6} m^{2}$ , suspended vertically from one end, has a length of 0.5 m at 100 $^{o}$ C. The rod is cooled to 0 $^{o}$ C .Young's modulus $=$ 10 $^{11}$ Nm $^{- 2}$ , coefficient of linear expansion $=$ 10 $^{- 5}$ K $^{- 1}$ and g $= 10 m s^{- 2}$
What mass must be attached at the lower end of the rod so that the rod is prevented from contracting on cooling?

40 kg

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30 kg

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20 kg

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10 kg

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Solution

The correct option is B 40 kg
$F o r c e = \frac{4 \times 10^{- 6} \times (5 \times 10^{- 4} \times 10^{11})}{0.5}$
$F = 400 N .$
now this force should be balanced by weight.
$⟹ m g = 400$
$⟹ m = \frac{400}{10}$ $= 40 k g$

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The correct option is B 40 kgForce=4×10−6×(5×10−4×1011)0.5F=400N.now this force should be balanced by weight.⟹mg=400⟹m=40010=40kg

The correct option is B 40 kg
$F o r c e = \frac{4 \times 10^{- 6} \times (5 \times 10^{- 4} \times 10^{11})}{0.5}$
$F = 400 N .$
now this force should be balanced by weight.
$⟹ m g = 400$
$⟹ m = \frac{400}{10}$ $= 40 k g$