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Q.

An iron rocket fragment initially at -100oC enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0.11 kcal/kg oC its melting point is 1535oC and the latent heat of fusion is 3 kcals/kg. The minimum velocity with which the fragment must have entered the atmosphere is

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a

0.45 km/s

b

1.32 km/s

c

2.32 km/s

d

zero

answer is B.

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Detailed Solution

The entire kinetic energy of the fragment is changed to heat. Expressing mass m in kilograms everywhere, we have12mv2=m(3)+m(0.11)1535∘+100∘4184v2=(8368)[3+180]≃1.76×106⇒v=(1.76)×103=1.32km/s
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An iron rocket fragment initially at -100oC enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0.11 kcal/kg oC its melting point is 1535oC and the latent heat of fusion is 3 kcals/kg. The minimum velocity with which the fragment must have entered the atmosphere is