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Question

A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, calculate the initial speed of the bullet. The initial temperature of the bullet is 27C and its melting point is 327C. Latent heat of fusion of lead = 2.5 × 104 J kg1 and specific heat capacity of lead = 125 J kg1 K1.


A

500 m/s

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B

5000 m/s

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C

100 m/s

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D

1000m/s

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Solution

The correct option is A

500 m/s


Let the mass of the bullet = m.

Heat required to take the bullet from 27C to 327C.

= m × (125Jkg1K1)(300K)

= m × (3.745 × 104 J kg1).

Heat required to melt the bullet

= m × (2.5 × 104Jkg1)

If the initial speed by v, the kinetic energy is 12mv2 and hence the heat developed is

12(12mv2) = 14mv2. Thus, 14mv2 = m(3.75+2.5) × 104Jkg1

or, v = 500 m s1.


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