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

Question

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, 0 . 45 km s - 1, 1 . 32 km s - 1, 2 . 32 km s - 1, Zero

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?