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An iron rocket fragment initially at - 100 ° C enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0 . 11 kcal kg - 1 ° C - 1 , its melting point is 1535 ° C and the latent heat of fusion is 3 kcal kg - 1 . The minimum velocity with which the fragment must have entered the atmosphere is

Options

  1. A0 . 45   km   s - 1
  2. B1 . 32   km   s - 1
  3. C2 . 32   km   s - 1
  4. DZero

Correct answer

B. 1 . 32   km   s - 1

Step-by-step solution

The kinetic energy of the fragment is changed to heat. Expressing mass m in kilograms everywher, we have 1 2 m v 2 = m 3 0 + m 0.11 1 5 3 5 ∘ + 1 0 0 ∘ 4 1 8 4 v 2 = 8 3 6 8 3 0 + 1 8 0 ≃ 1.76 × 1 0 6 Hence v = 1.76 × 1 0 3 = 1.32 km s - 1

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