A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is: (Given initial temperature of the bullet = 127°C), Melting point of the bullet = 327°C, Latent heat of fusion of lead = \(2.5 × 10^4 J kg^{–1}\) Specific heat capacity of lead = 125 J/kg K)
- \(125\;ms^{–1}\)
- \(500\;ms^{–1}\)
- \(250\;ms^{–1}\)
- \(600\;ms^{–1}\)
The Correct Option is B
Solution and Explanation
The initial speed of bullet is:
\(\frac{2}{5}×\frac{1}{2}mv^2=mL+msΔT\)
\(⇒\frac{v^2}{5}=2.5×10 ^4+125+200\)
\(⇒\frac{v^2}{5}=5×10^4\)
\(⇒ v = 500 \;m/s\)
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
